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Common Core: High School - Algebra : High School: Algebra

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 #48 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 10 b\right)^{2}$

Possible Answers:

$a^{2} + 20 a b + 100 b^{2}$

$10 a b + 100 b^{2}$

$a^{2} + 20 a b$

$b^{2}$

$a^{2}$

Correct answer:

$a^{2} + 20 a b + 100 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 10 b\right)^{2}= \left(a + 10*b\right) \cdot \left(a + 10*b\right)$

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.

$a\cdot10 b=10 a b$

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

$a\cdot10 b=10 a b$

Now we multiply the last terms of each expression together.

$10 b\cdot10 b=100 b^{2}$

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

$a^{2} + 20 a b + 100 b^{2}$

Report an Error

Example Question #51 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

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

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

$a^{2}$

$b^{2}$

$a^{2} + 18 a b$

Correct answer:

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

Explanation:

The first step is to rewrite the problem as follows.

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

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.

$a\cdot9 b=9 a b$

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

$a\cdot9 b=9 a b$

Now we multiply the last terms of each expression together.

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

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

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

Report an Error

Example Question #221 : Arithmetic With Polynomials & Rational Expressions

Use FOIL for the following expression.

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

Possible Answers:

$a^{2}$

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

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

$b^{2}$

$a^{2} + 12 a b$

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 #291 : High School: Algebra

Use FOIL for the following expression.

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

Possible Answers:

$a b + b^{2}$

$a^{2} + 2 a b$

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

$b^{2}$

$a^{2}$

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 #52 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

$a^{2} + 2 a b$

$a^{2}$

$a b + b^{2}$

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

$b^{2}$

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 #53 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

$a^{2} + 38 a b$

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

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

$a^{2}$

$b^{2}$

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:

$a b + b^{2}$

$a^{2} + 2 a b$

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

$b^{2}$

$a^{2}$

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 #54 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

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

$a^{2}$

$b^{2}$

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

$a^{2} + 38 a b$

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 #55 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

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

$a^{2}$

$a^{2} + 26 a b$

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

$b^{2}$

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 #56 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

$b^{2}$

$a^{2} + 26 a b$

$a^{2}$

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

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

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

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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

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Common Core: High School - Algebra : High School: Algebra

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

All Common Core: High School - Algebra Resources

Example Questions

Example Question #48 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #51 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #221 : Arithmetic With Polynomials & Rational Expressions

Example Question #291 : High School: Algebra

Example Question #52 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #53 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #225 : Arithmetic With Polynomials & Rational Expressions

Example Question #54 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #55 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #56 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

All Common Core: High School - Algebra Resources

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