Solve (x+4)(x+4)(2x-2)

$$(x+4)(x+4)(2x-2)$$

Evaluate

$$2\left(x-1\right)\left(x+4\right)^{2}$$

Solution Steps

Multiply x+4 and x+4 to get \left(x+4\right)^{2}.

$$\left(x+4\right)^{2}\left(2x-2\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$\left(x^{2}+8x+16\right)\left(2x-2\right)$$

Apply the distributive property by multiplying each term of x^{2}+8x+16 by each term of 2x-2.

$$2x^{3}-2x^{2}+16x^{2}-16x+32x-32$$

Combine -2x^{2} and 16x^{2} to get 14x^{2}.

$$2x^{3}+14x^{2}-16x+32x-32$$

Combine -16x and 32x to get 16x.

$$2x^{3}+14x^{2}+16x-32$$

Expand

$$2x^{3}+14x^{2}+16x-32$$

Solution Steps

Multiply x+4 and x+4 to get \left(x+4\right)^{2}.

$$\left(x+4\right)^{2}\left(2x-2\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$\left(x^{2}+8x+16\right)\left(2x-2\right)$$

Apply the distributive property by multiplying each term of x^{2}+8x+16 by each term of 2x-2.

$$2x^{3}-2x^{2}+16x^{2}-16x+32x-32$$

Combine -2x^{2} and 16x^{2} to get 14x^{2}.

$$2x^{3}+14x^{2}-16x+32x-32$$

Combine -16x and 32x to get 16x.

$$2x^{3}+14x^{2}+16x-32$$