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Common Core: High School - Algebra : Arithmetic with Polynomials & Rational Expressions

Study concepts, example questions & explanations for Common Core: High School - Algebra

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All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #191 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 17 b\right)^{2}$ $\displaystyle \left(a + 17 b\right)^{2}$

Possible Answers:

$a^{2} + 34 a b$ $\displaystyle a^{2} + 34 a b$

$a^{2} + 34 a b + 289 b^{2}$ $\displaystyle a^{2} + 34 a b + 289 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

$a^{2}$ $\displaystyle a^{2}$

$17 a b + 289 b^{2}$ $\displaystyle 17 a b + 289 b^{2}$

Correct answer:

$a^{2} + 34 a b + 289 b^{2}$ $\displaystyle a^{2} + 34 a b + 289 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 17 b\right)^{2}= \left(a + 17*b\right) \cdot \left(a + 17*b\right)$ $\displaystyle \left(a + 17 b\right)^{2}= \left(a + 17*b\right) \cdot \left(a + 17*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot17 b=17 a b$ $\displaystyle a\cdot17 b=17 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot17 b=17 a b$ $\displaystyle a\cdot17 b=17 a b$

Now we multiply the last terms of each expression together.

$17 b\cdot17 b=289 b^{2}$ $\displaystyle 17 b\cdot17 b=289 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 34 a b + 289 b^{2}$ $\displaystyle a^{2} + 34 a b + 289 b^{2}$

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Example Question #192 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 4 b\right)^{2}$ $\displaystyle \left(a + 4 b\right)^{2}$

Possible Answers:

$4 a b + 16 b^{2}$ $\displaystyle 4 a b + 16 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

$a^{2} + 8 a b$ $\displaystyle a^{2} + 8 a b$

$a^{2}$ $\displaystyle a^{2}$

$a^{2} + 8 a b + 16 b^{2}$ $\displaystyle a^{2} + 8 a b + 16 b^{2}$

Correct answer:

$a^{2} + 8 a b + 16 b^{2}$ $\displaystyle a^{2} + 8 a b + 16 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 4 b\right)^{2}= \left(a + 4*b\right) \cdot \left(a + 4*b\right)$ $\displaystyle \left(a + 4 b\right)^{2}= \left(a + 4*b\right) \cdot \left(a + 4*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot4 b=4 a b$ $\displaystyle a\cdot4 b=4 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot4 b=4 a b$ $\displaystyle a\cdot4 b=4 a b$

Now we multiply the last terms of each expression together.

$4 b\cdot4 b=16 b^{2}$ $\displaystyle 4 b\cdot4 b=16 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 8 a b + 16 b^{2}$ $\displaystyle a^{2} + 8 a b + 16 b^{2}$

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Example Question #193 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 15 b\right)^{2}$ $\displaystyle \left(a + 15 b\right)^{2}$

Possible Answers:

$b^{2}$ $\displaystyle b^{2}$

$a^{2}$ $\displaystyle a^{2}$

$a^{2} + 30 a b + 225 b^{2}$ $\displaystyle a^{2} + 30 a b + 225 b^{2}$

$a^{2} + 30 a b$ $\displaystyle a^{2} + 30 a b$

$15 a b + 225 b^{2}$ $\displaystyle 15 a b + 225 b^{2}$

Correct answer:

$a^{2} + 30 a b + 225 b^{2}$ $\displaystyle a^{2} + 30 a b + 225 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 15 b\right)^{2}= \left(a + 15*b\right) \cdot \left(a + 15*b\right)$ $\displaystyle \left(a + 15 b\right)^{2}= \left(a + 15*b\right) \cdot \left(a + 15*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot15 b=15 a b$ $\displaystyle a\cdot15 b=15 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot15 b=15 a b$ $\displaystyle a\cdot15 b=15 a b$

Now we multiply the last terms of each expression together.

$15 b\cdot15 b=225 b^{2}$ $\displaystyle 15 b\cdot15 b=225 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 30 a b + 225 b^{2}$ $\displaystyle a^{2} + 30 a b + 225 b^{2}$

Report an Error

Example Question #194 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 16 b\right)^{2}$ $\displaystyle \left(a + 16 b\right)^{2}$

Possible Answers:

$16 a b + 256 b^{2}$ $\displaystyle 16 a b + 256 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

$a^{2} + 32 a b + 256 b^{2}$ $\displaystyle a^{2} + 32 a b + 256 b^{2}$

$a^{2} + 32 a b$ $\displaystyle a^{2} + 32 a b$

$a^{2}$ $\displaystyle a^{2}$

Correct answer:

$a^{2} + 32 a b + 256 b^{2}$ $\displaystyle a^{2} + 32 a b + 256 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 16 b\right)^{2}= \left(a + 16*b\right) \cdot \left(a + 16*b\right)$ $\displaystyle \left(a + 16 b\right)^{2}= \left(a + 16*b\right) \cdot \left(a + 16*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot16 b=16 a b$ $\displaystyle a\cdot16 b=16 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot16 b=16 a b$ $\displaystyle a\cdot16 b=16 a b$

Now we multiply the last terms of each expression together.

$16 b\cdot16 b=256 b^{2}$ $\displaystyle 16 b\cdot16 b=256 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 32 a b + 256 b^{2}$ $\displaystyle a^{2} + 32 a b + 256 b^{2}$

Report an Error

Example Question #193 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 9 b\right)^{2}$ $\displaystyle \left(a + 9 b\right)^{2}$

Possible Answers:

$9 a b + 81 b^{2}$ $\displaystyle 9 a b + 81 b^{2}$

$a^{2} + 18 a b$ $\displaystyle a^{2} + 18 a b$

$b^{2}$ $\displaystyle b^{2}$

$a^{2} + 18 a b + 81 b^{2}$ $\displaystyle a^{2} + 18 a b + 81 b^{2}$

$a^{2}$ $\displaystyle a^{2}$

Correct answer:

$a^{2} + 18 a b + 81 b^{2}$ $\displaystyle a^{2} + 18 a b + 81 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 9 b\right)^{2}= \left(a + 9*b\right) \cdot \left(a + 9*b\right)$ $\displaystyle \left(a + 9 b\right)^{2}= \left(a + 9*b\right) \cdot \left(a + 9*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot9 b=9 a b$ $\displaystyle a\cdot9 b=9 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot9 b=9 a b$ $\displaystyle a\cdot9 b=9 a b$

Now we multiply the last terms of each expression together.

$9 b\cdot9 b=81 b^{2}$ $\displaystyle 9 b\cdot9 b=81 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 18 a b + 81 b^{2}$ $\displaystyle a^{2} + 18 a b + 81 b^{2}$

Report an Error

Example Question #196 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 13 b\right)^{2}$ $\displaystyle \left(a + 13 b\right)^{2}$

Possible Answers:

$b^{2}$ $\displaystyle b^{2}$

$13 a b + 169 b^{2}$ $\displaystyle 13 a b + 169 b^{2}$

$a^{2}$ $\displaystyle a^{2}$

$a^{2} + 26 a b$ $\displaystyle a^{2} + 26 a b$

$a^{2} + 26 a b + 169 b^{2}$ $\displaystyle a^{2} + 26 a b + 169 b^{2}$

Correct answer:

$a^{2} + 26 a b + 169 b^{2}$ $\displaystyle a^{2} + 26 a b + 169 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 13 b\right)^{2}= \left(a + 13*b\right) \cdot \left(a + 13*b\right)$ $\displaystyle \left(a + 13 b\right)^{2}= \left(a + 13*b\right) \cdot \left(a + 13*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot13 b=13 a b$ $\displaystyle a\cdot13 b=13 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot13 b=13 a b$ $\displaystyle a\cdot13 b=13 a b$

Now we multiply the last terms of each expression together.

$13 b\cdot13 b=169 b^{2}$ $\displaystyle 13 b\cdot13 b=169 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 26 a b + 169 b^{2}$ $\displaystyle a^{2} + 26 a b + 169 b^{2}$

Report an Error

Example Question #197 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 13 b\right)^{2}$ $\displaystyle \left(a + 13 b\right)^{2}$

Possible Answers:

$a^{2}$ $\displaystyle a^{2}$

$13 a b + 169 b^{2}$ $\displaystyle 13 a b + 169 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

$a^{2} + 26 a b + 169 b^{2}$ $\displaystyle a^{2} + 26 a b + 169 b^{2}$

$a^{2} + 26 a b$ $\displaystyle a^{2} + 26 a b$

Correct answer:

$a^{2} + 26 a b + 169 b^{2}$ $\displaystyle a^{2} + 26 a b + 169 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 13 b\right)^{2}= \left(a + 13*b\right) \cdot \left(a + 13*b\right)$ $\displaystyle \left(a + 13 b\right)^{2}= \left(a + 13*b\right) \cdot \left(a + 13*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot13 b=13 a b$ $\displaystyle a\cdot13 b=13 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot13 b=13 a b$ $\displaystyle a\cdot13 b=13 a b$

Now we multiply the last terms of each expression together.

$13 b\cdot13 b=169 b^{2}$ $\displaystyle 13 b\cdot13 b=169 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 26 a b + 169 b^{2}$ $\displaystyle a^{2} + 26 a b + 169 b^{2}$

Report an Error

Example Question #194 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 12 b\right)^{2}$ $\displaystyle \left(a + 12 b\right)^{2}$

Possible Answers:

$a^{2} + 24 a b$ $\displaystyle a^{2} + 24 a b$

$a^{2}$ $\displaystyle a^{2}$

$a^{2} + 24 a b + 144 b^{2}$ $\displaystyle a^{2} + 24 a b + 144 b^{2}$

$12 a b + 144 b^{2}$ $\displaystyle 12 a b + 144 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

Correct answer:

$a^{2} + 24 a b + 144 b^{2}$ $\displaystyle a^{2} + 24 a b + 144 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 12 b\right)^{2}= \left(a + 12*b\right) \cdot \left(a + 12*b\right)$ $\displaystyle \left(a + 12 b\right)^{2}= \left(a + 12*b\right) \cdot \left(a + 12*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot12 b=12 a b$ $\displaystyle a\cdot12 b=12 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot12 b=12 a b$ $\displaystyle a\cdot12 b=12 a b$

Now we multiply the last terms of each expression together.

$12 b\cdot12 b=144 b^{2}$ $\displaystyle 12 b\cdot12 b=144 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 24 a b + 144 b^{2}$ $\displaystyle a^{2} + 24 a b + 144 b^{2}$

Report an Error

Example Question #199 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 12 b\right)^{2}$ $\displaystyle \left(a + 12 b\right)^{2}$

Possible Answers:

$12 a b + 144 b^{2}$ $\displaystyle 12 a b + 144 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

$a^{2}$ $\displaystyle a^{2}$

$a^{2} + 24 a b + 144 b^{2}$ $\displaystyle a^{2} + 24 a b + 144 b^{2}$

$a^{2} + 24 a b$ $\displaystyle a^{2} + 24 a b$

Correct answer:

$a^{2} + 24 a b + 144 b^{2}$ $\displaystyle a^{2} + 24 a b + 144 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 12 b\right)^{2}= \left(a + 12*b\right) \cdot \left(a + 12*b\right)$ $\displaystyle \left(a + 12 b\right)^{2}= \left(a + 12*b\right) \cdot \left(a + 12*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot12 b=12 a b$ $\displaystyle a\cdot12 b=12 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot12 b=12 a b$ $\displaystyle a\cdot12 b=12 a b$

Now we multiply the last terms of each expression together.

$12 b\cdot12 b=144 b^{2}$ $\displaystyle 12 b\cdot12 b=144 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 24 a b + 144 b^{2}$ $\displaystyle a^{2} + 24 a b + 144 b^{2}$

Report an Error

Example Question #200 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 14 b\right)^{2}$ $\displaystyle \left(a + 14 b\right)^{2}$

Possible Answers:

$14 a b + 196 b^{2}$ $\displaystyle 14 a b + 196 b^{2}$

$b^{2}$ $\displaystyle b^{2}$

$a^{2} + 28 a b$ $\displaystyle a^{2} + 28 a b$

$a^{2}$ $\displaystyle a^{2}$

$a^{2} + 28 a b + 196 b^{2}$ $\displaystyle a^{2} + 28 a b + 196 b^{2}$

Correct answer:

$a^{2} + 28 a b + 196 b^{2}$ $\displaystyle a^{2} + 28 a b + 196 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 14 b\right)^{2}= \left(a + 14*b\right) \cdot \left(a + 14*b\right)$ $\displaystyle \left(a + 14 b\right)^{2}= \left(a + 14*b\right) \cdot \left(a + 14*b\right)$

Now we multiply the first parts of the first and second expression together.

$a\cdota=a^{2}$ $\displaystyle a\cdota=a^{2}$

Now we multiply the first term of the first expression with the second term of the second expression.

$a\cdot14 b=14 a b$ $\displaystyle a\cdot14 b=14 a b$

Now we multiply the second term of the first expression with the first term of the second expression.

$a\cdot14 b=14 a b$ $\displaystyle a\cdot14 b=14 a b$

Now we multiply the last terms of each expression together.

$14 b\cdot14 b=196 b^{2}$ $\displaystyle 14 b\cdot14 b=196 b^{2}$

Now we add all these results together, and we get.

$a^{2} + 28 a b + 196 b^{2}$ $\displaystyle a^{2} + 28 a b + 196 b^{2}$

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All Common Core: High School - Algebra Resources

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Common Core: High School - Algebra : Arithmetic with Polynomials & Rational Expressions

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #191 : Arithmetic With Polynomials & Rational Expressions

Example Question #192 : Arithmetic With Polynomials & Rational Expressions

Example Question #193 : Arithmetic With Polynomials & Rational Expressions

Example Question #194 : Arithmetic With Polynomials & Rational Expressions

Example Question #193 : Arithmetic With Polynomials & Rational Expressions

Example Question #196 : Arithmetic With Polynomials & Rational Expressions

Example Question #197 : Arithmetic With Polynomials & Rational Expressions

Example Question #194 : Arithmetic With Polynomials & Rational Expressions

Example Question #199 : Arithmetic With Polynomials & Rational Expressions

Example Question #200 : Arithmetic With Polynomials & Rational Expressions

All Common Core: High School - Algebra Resources

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