Common Core: High School - Algebra : Polynomial Identities and Numerical Relationships: CCSS.Math.Content.HSA-APR.C.4

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

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All Common Core: High School - Algebra Resources

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Example Questions

Example Question #31 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2}\)

\(\displaystyle 14 a b + 196 b^{2}\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

\(\displaystyle a^{2} + 28 a b\)

Correct answer:

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot14 b=14 a b\)

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

\(\displaystyle a\cdot14 b=14 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 14 b\cdot14 b=196 b^{2}\)

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

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Example Question #32 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2}\)

\(\displaystyle 13 a b + 169 b^{2}\)

\(\displaystyle a^{2} + 26 a b\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2} + 26 a b + 169 b^{2}\)

Correct answer:

\(\displaystyle a^{2} + 26 a b + 169 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot13 b=13 a b\)

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

\(\displaystyle a\cdot13 b=13 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 13 b\cdot13 b=169 b^{2}\)

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

\(\displaystyle a^{2} + 26 a b + 169 b^{2}\)

Example Question #33 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2} + 28 a b\)

\(\displaystyle 14 a b + 196 b^{2}\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2}\)

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Correct answer:

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot14 b=14 a b\)

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

\(\displaystyle a\cdot14 b=14 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 14 b\cdot14 b=196 b^{2}\)

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

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Example Question #34 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2} + 8 a b + 16 b^{2}\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2}\)

\(\displaystyle a^{2} + 8 a b\)

\(\displaystyle 4 a b + 16 b^{2}\)

Correct answer:

\(\displaystyle a^{2} + 8 a b + 16 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot4 b=4 a b\)

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

\(\displaystyle a\cdot4 b=4 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 4 b\cdot4 b=16 b^{2}\)

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

\(\displaystyle a^{2} + 8 a b + 16 b^{2}\)

Example Question #35 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2} + 28 a b\)

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

\(\displaystyle 14 a b + 196 b^{2}\)

\(\displaystyle a^{2}\)

\(\displaystyle b^{2}\)

Correct answer:

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot14 b=14 a b\)

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

\(\displaystyle a\cdot14 b=14 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 14 b\cdot14 b=196 b^{2}\)

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

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Example Question #36 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle 18 a b + 324 b^{2}\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2}\)

\(\displaystyle a^{2} + 36 a b\)

\(\displaystyle a^{2} + 36 a b + 324 b^{2}\)

Correct answer:

\(\displaystyle a^{2} + 36 a b + 324 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot18 b=18 a b\)

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

\(\displaystyle a\cdot18 b=18 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 18 b\cdot18 b=324 b^{2}\)

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

\(\displaystyle a^{2} + 36 a b + 324 b^{2}\)

Example Question #37 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2}\)

\(\displaystyle 13 a b + 169 b^{2}\)

\(\displaystyle a^{2} + 26 a b + 169 b^{2}\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2} + 26 a b\)

Correct answer:

\(\displaystyle a^{2} + 26 a b + 169 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot13 b=13 a b\)

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

\(\displaystyle a\cdot13 b=13 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 13 b\cdot13 b=169 b^{2}\)

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

\(\displaystyle a^{2} + 26 a b + 169 b^{2}\)

Example Question #38 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle b^{2}\)

\(\displaystyle 14 a b + 196 b^{2}\)

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

\(\displaystyle a^{2}\)

\(\displaystyle a^{2} + 28 a b\)

Correct answer:

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot14 b=14 a b\)

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

\(\displaystyle a\cdot14 b=14 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 14 b\cdot14 b=196 b^{2}\)

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

\(\displaystyle a^{2} + 28 a b + 196 b^{2}\)

Example Question #39 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

\(\displaystyle a^{2} + 38 a b + 361 b^{2}\)

\(\displaystyle a^{2}\)

\(\displaystyle 19 a b + 361 b^{2}\)

\(\displaystyle b^{2}\)

\(\displaystyle a^{2} + 38 a b\)

Correct answer:

\(\displaystyle a^{2} + 38 a b + 361 b^{2}\)

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot19 b=19 a b\)

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

\(\displaystyle a\cdot19 b=19 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 19 b\cdot19 b=361 b^{2}\)

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

\(\displaystyle a^{2} + 38 a b + 361 b^{2}\)

Example Question #31 : Polynomial Identities And Numerical Relationships: Ccss.Math.Content.Hsa Apr.C.4

Use FOIL for the following expression.

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

Possible Answers:

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

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

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

\(\displaystyle a^{2}\)

\(\displaystyle b^{2}\)

Correct answer:

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

Explanation:

The first step is to rewrite the problem as follows.

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

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

\(\displaystyle a\cdota=a^{2}\)

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

\(\displaystyle a\cdot2 b=2 a b\)

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

\(\displaystyle a\cdot2 b=2 a b\)

Now we multiply the last terms of each expression together.

\(\displaystyle 2 b\cdot2 b=4 b^{2}\)

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

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

All Common Core: High School - Algebra Resources

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