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

Use FOIL for the following expression.

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

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

$a^{2}$

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

$a^{2} + 6 a b$

$b^{2}$

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.

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

Use FOIL for the following expression.

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

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

$a^{2}$

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

$a^{2} + 24 a b$

$b^{2}$

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.

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

Use FOIL for the following expression.

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

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

$a^{2}$

$14 a b + 196 b^{2}$

$a^{2} + 28 a b$

$b^{2}$

Explanation

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdot14 b=14 a b$

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

$a\cdot14 b=14 a b$

Now we multiply the last terms of each expression together.

$14 b\cdot14 b=196 b^{2}$

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

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

Use FOIL for the following expression.

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

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

$a^{2}$

$14 a b + 196 b^{2}$

$a^{2} + 28 a b$

$b^{2}$

Explanation

The first step is to rewrite the problem as follows.

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

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

$a\cdota=a^{2}$

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

$a\cdot14 b=14 a b$

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

$a\cdot14 b=14 a b$

Now we multiply the last terms of each expression together.

$14 b\cdot14 b=196 b^{2}$

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

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

Use FOIL for the following expression.

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

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

$a^{2}$

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

$a^{2} + 24 a b$

$b^{2}$

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.

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

Use FOIL for the following expression.

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

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

$a^{2}$

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

$a^{2} + 4 a b$

$b^{2}$

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.

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

Use FOIL for the following expression.

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

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

$a^{2}$

$15 a b + 225 b^{2}$

$a^{2} + 30 a b$

$b^{2}$

Explanation

The first step is to rewrite the problem as follows.

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

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.

$a \cdot 15 b = 15 a b$

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.

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

Use FOIL for the following expression.

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

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

$a^{2}$

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

$a^{2} + 16 a b$

$b^{2}$

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.

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

Use FOIL for the following expression.

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

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

$a^{2}$

$15 a b + 225 b^{2}$

$a^{2} + 30 a b$

$b^{2}$

Explanation

The first step is to rewrite the problem as follows.

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

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.

$a\cdot15 b=15 a b$

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

$a\cdot15 b=15 a b$

Now we multiply the last terms of each expression together.

$15 b\cdot15 b=225 b^{2}$

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

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

Use FOIL for the following expression.

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

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

$a^{2}$

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

$a^{2} + 26 a b$

$b^{2}$

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.

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

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

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