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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 #221 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 6 b\right)^{2}$

Possible Answers:

$a^{2} + 12 a b$

$b^{2}$

$a^{2} + 12 a b + 36 b^{2}$

$a^{2}$

$6 a b + 36 b^{2}$

Correct answer:

$a^{2} + 12 a b + 36 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 6 b\right)^{2}= \left(a + 6*b\right) \cdot \left(a + 6*b\right)$

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

$a\cdota=a^{2}$

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

$a\cdot6 b=6 a b$

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

$a\cdot6 b=6 a b$

Now we multiply the last terms of each expression together.

$6 b\cdot6 b=36 b^{2}$

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

$a^{2} + 12 a b + 36 b^{2}$

Report an Error

Example Question #222 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

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

Possible Answers:

$a^{2} + 2 a b$

$b^{2}$

$a^{2}$

$a b + b^{2}$

$a^{2} + 2 a b + b^{2}$

Correct answer:

$a^{2} + 2 a b + b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdotb=a b$

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

$a\cdotb=a b$

Now we multiply the last terms of each expression together.

$b\cdotb=b^{2}$

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

$a^{2} + 2 a b + b^{2}$

Report an Error

Example Question #223 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

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

Possible Answers:

$b^{2}$

$a^{2}$

$a b + b^{2}$

$a^{2} + 2 a b + b^{2}$

$a^{2} + 2 a b$

Correct answer:

$a^{2} + 2 a b + b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdotb=a b$

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

$a\cdotb=a b$

Now we multiply the last terms of each expression together.

$b\cdotb=b^{2}$

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

$a^{2} + 2 a b + b^{2}$

Report an Error

Example Question #224 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 19 b\right)^{2}$

Possible Answers:

$a^{2}$

$19 a b + 361 b^{2}$

$b^{2}$

$a^{2} + 38 a b + 361 b^{2}$

$a^{2} + 38 a b$

Correct answer:

$a^{2} + 38 a b + 361 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 19 b\right)^{2}= \left(a + 19*b\right) \cdot \left(a + 19*b\right)$

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

$a\cdota=a^{2}$

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

$a\cdot19 b=19 a b$

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

$a\cdot19 b=19 a b$

Now we multiply the last terms of each expression together.

$19 b\cdot19 b=361 b^{2}$

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

$a^{2} + 38 a b + 361 b^{2}$

Report an Error

Example Question #225 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

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

Possible Answers:

$b^{2}$

$a^{2} + 2 a b$

$a^{2}$

$a b + b^{2}$

$a^{2} + 2 a b + b^{2}$

Correct answer:

$a^{2} + 2 a b + b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdotb=a b$

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

$a\cdotb=a b$

Now we multiply the last terms of each expression together.

$b\cdotb=b^{2}$

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

$a^{2} + 2 a b + b^{2}$

Report an Error

Example Question #226 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

$\left(a + 19 b\right)^{2}$

Possible Answers:

$a^{2} + 38 a b + 361 b^{2}$

$b^{2}$

$19 a b + 361 b^{2}$

$a^{2}$

$a^{2} + 38 a b$

Correct answer:

$a^{2} + 38 a b + 361 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 19 b\right)^{2}= \left(a + 19*b\right) \cdot \left(a + 19*b\right)$

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

$a\cdota=a^{2}$

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

$a\cdot19 b=19 a b$

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

$a\cdot19 b=19 a b$

Now we multiply the last terms of each expression together.

$19 b\cdot19 b=361 b^{2}$

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

$a^{2} + 38 a b + 361 b^{2}$

Report an Error

Example Question #227 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

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

Possible Answers:

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

$a^{2} + 26 a b$

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

$b^{2}$

$a^{2}$

Correct answer:

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

Explanation:

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdot13 b=13 a b$

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

$a\cdot13 b=13 a b$

Now we multiply the last terms of each expression together.

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

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

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

Report an Error

Example Question #228 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

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

Possible Answers:

$a^{2} + 26 a b$

$b^{2}$

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

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

$a^{2}$

Correct answer:

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

Explanation:

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdot13 b=13 a b$

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

$a\cdot13 b=13 a b$

Now we multiply the last terms of each expression together.

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

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

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

Report an Error

Example Question #301 : High School: Algebra

Use FOIL for the following expression.

$\left(a + 18 b\right)^{2}$

Possible Answers:

$a^{2}$

$18 a b + 324 b^{2}$

$a^{2} + 36 a b$

$a^{2} + 36 a b + 324 b^{2}$

$b^{2}$

Correct answer:

$a^{2} + 36 a b + 324 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 18 b\right)^{2}= \left(a + 18*b\right) \cdot \left(a + 18*b\right)$

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

$a\cdota=a^{2}$

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

$a\cdot18 b=18 a b$

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

$a\cdot18 b=18 a b$

Now we multiply the last terms of each expression together.

$18 b\cdot18 b=324 b^{2}$

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

$a^{2} + 36 a b + 324 b^{2}$

Report an Error

Example Question #301 : High School: Algebra

Use FOIL for the following expression.

$\left(a + 8 b\right)^{2}$

Possible Answers:

$8 a b + 64 b^{2}$

$b^{2}$

$a^{2} + 16 a b + 64 b^{2}$

$a^{2} + 16 a b$

$a^{2}$

Correct answer:

$a^{2} + 16 a b + 64 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 8 b\right)^{2}= \left(a + 8*b\right) \cdot \left(a + 8*b\right)$

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

$a\cdota=a^{2}$

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

$a\cdot8 b=8 a b$

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

$a\cdot8 b=8 a b$

Now we multiply the last terms of each expression together.

$8 b\cdot8 b=64 b^{2}$

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

$a^{2} + 16 a b + 64 b^{2}$

Report an Error

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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 #221 : Arithmetic With Polynomials & Rational Expressions

Example Question #222 : Arithmetic With Polynomials & Rational Expressions

Example Question #223 : Arithmetic With Polynomials & Rational Expressions

Example Question #224 : Arithmetic With Polynomials & Rational Expressions

Example Question #225 : Arithmetic With Polynomials & Rational Expressions

Example Question #226 : Arithmetic With Polynomials & Rational Expressions

Example Question #227 : Arithmetic With Polynomials & Rational Expressions

Example Question #228 : Arithmetic With Polynomials & Rational Expressions

Example Question #301 : High School: Algebra

Example Question #301 : High School: Algebra

All Common Core: High School - Algebra Resources

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