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

Use FOIL for the following expression.

$\left(a + 5 b\right)^{2}$

Possible Answers:

$a^{2}$

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

$b^{2}$

$a^{2} + 10 a b + 25 b^{2}$

$5 a b + 25 b^{2}$

Correct answer:

$a^{2} + 10 a b + 25 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 5 b\right)^{2} = \left( a + 5*b \right) \cdot \left( a + 5*b \right)$

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

$a \cdot a = a^{2}$

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

$a \cdot 5 b = 5 a b$

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

$a \cdot 5 b = 5 a b$

Now we multiply the last terms of each expression together.

$5 b \cdot 5 b = 25 b^{2}$

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

$a^{2} + 10 a b + 25 b^{2}$

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Example Question #11 : 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:

$a^{2} + 2 a b$

$a^{2}$

$a b + b^{2}$

$b^{2}$

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

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.

$a \cdot a = a^{2}$

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

$a \cdot b = a b$

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

$a \cdot b = a b$

Now we multiply the last terms of each expression together.

$b \cdot b = b^{2}$

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

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

Report an Error

Example Question #12 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 3 b\right)^{2}$

Possible Answers:

$a^{2}$

$3 a b + 9 b^{2}$

$b^{2}$

$a^{2} + 6 a b$

$a^{2} + 6 a b + 9 b^{2}$

Correct answer:

$a^{2} + 6 a b + 9 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 3 b\right)^{2}= \left(a + 3*b\right) \cdot \left(a + 3*b\right)$

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.

$a\cdot3 b=3 a b$

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

$a\cdot3 b=3 a b$

Now we multiply the last terms of each expression together.

$3 b\cdot3 b=9 b^{2}$

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

$a^{2} + 6 a b + 9 b^{2}$

Report an Error

Example Question #12 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

$a^{2}$

$2 a b + 4 b^{2}$

$a^{2} + 4 a b$

$a^{2} + 4 a b + 4 b^{2}$

$b^{2}$

Correct answer:

$a^{2} + 4 a b + 4 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

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

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.

$a\cdot2 b=2 a b$

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

$a\cdot2 b=2 a b$

Now we multiply the last terms of each expression together.

$2 b\cdot2 b=4 b^{2}$

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

$a^{2} + 4 a b + 4 b^{2}$

Report an Error

Example Question #13 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

$\left(a + 7 b\right)^{2}$

Possible Answers:

$7 a b + 49 b^{2}$

$a^{2}$

$a^{2} + 14 a b + 49 b^{2}$

$a^{2} + 14 a b$

$b^{2}$

Correct answer:

$a^{2} + 14 a b + 49 b^{2}$

Explanation:

The first step is to rewrite the problem as follows.

$\left(a + 7 b\right)^{2}= \left(a + 7*b\right) \cdot \left(a + 7*b\right)$

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.

$a\cdot7 b=7 a b$

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

$a\cdot7 b=7 a b$

Now we multiply the last terms of each expression together.

$7 b\cdot7 b=49 b^{2}$

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

$a^{2} + 14 a b + 49 b^{2}$

Report an Error

Example Question #15 : 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:

$a^{2}$

$a^{2} + 2 a b$

$b^{2}$

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

$a b + b^{2}$

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

Use FOIL for the following expression.

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

Possible Answers:

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

$b^{2}$

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

$a^{2}$

$a^{2} + 24 a b$

Correct answer:

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

Explanation:

The first step is to rewrite the problem as follows.

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

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.

$a\cdot12 b=12 a b$

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

$a\cdot12 b=12 a b$

Now we multiply the last terms of each expression together.

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

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

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

Report an Error

Example Question #17 : 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:

$a^{2} + 26 a b$

$a^{2}$

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

$b^{2}$

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

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

Example Question #14 : 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:

$a^{2}$

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

$b^{2}$

$a^{2} + 18 a b$

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

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

Use FOIL for the following expression.

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

Possible Answers:

$a^{2} + 16 a b$

$b^{2}$

$a^{2}$

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

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

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

Example Question #11 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #12 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #12 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #13 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #15 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #16 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #17 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #14 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Example Question #15 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

All Common Core: High School - Algebra Resources

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