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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 10 b = 10 a b$

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

$a \cdot 10 b = 10 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 14 b = 14 a b$

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

$a \cdot 14 b = 14 a b$

Now we multiply the last terms of each expression together.

$14 b \cdot 14 b = 196 b^{2}$

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

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

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Question

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

Which of the following expressions is equivalent to the expression above?

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 18 b = 18 a b$

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

$a \cdot 18 b = 18 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 2 b = 2 a b$

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

$a \cdot 2 b = 2 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 17 b = 17 a b$

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

$a \cdot 17 b = 17 a b$

Now we multiply the last terms of each expression together.

$17 b \cdot 17 b = 289 b^{2}$

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 3 b = 3 a b$

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

$a \cdot 3 b = 3 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 2 b = 2 a b$

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

$a \cdot 2 b = 2 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 15 b = 15 a b$

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

$a \cdot 15 b = 15 a b$

Now we multiply the last terms of each expression together.

$15 b \cdot 15 b = 225 b^{2}$

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 7 b = 7 a b$

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

$a \cdot 7 b = 7 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a\cdot4 b=4 a b$

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

$a\cdot4 b=4 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 6 b = 6 a b$

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

$a \cdot 6 b = 6 a b$

Now we multiply the last terms of each expression together.

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

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

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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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Question

Use FOIL for the following expression.

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

Answer

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.

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

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

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Question

Use FOIL for the following expression.

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

Answer

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.

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

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

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Question

Use FOIL for the following expression.

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

Answer

The first step is to rewrite the problem as follows.

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

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.

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

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