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

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

Evaluate

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

Solution Steps

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

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

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

$$\left(x-4\right)\left(x^{2}+8x+16\right)+2$$

Apply the distributive property by multiplying each term of x-4 by each term of x^{2}+8x+16.

$$x^{3}+8x^{2}+16x-4x^{2}-32x-64+2$$

Combine 8x^{2} and -4x^{2} to get 4x^{2}.

$$x^{3}+4x^{2}+16x-32x-64+2$$

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

$$x^{3}+4x^{2}-16x-64+2$$

Add -64 and 2 to get -62.

$$x^{3}+4x^{2}-16x-62$$

Expand

$$x^{3}+4x^{2}-16x-62$$

Solution Steps

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

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

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

$$\left(x-4\right)\left(x^{2}+8x+16\right)+2$$

Apply the distributive property by multiplying each term of x-4 by each term of x^{2}+8x+16.

$$x^{3}+8x^{2}+16x-4x^{2}-32x-64+2$$

Combine 8x^{2} and -4x^{2} to get 4x^{2}.

$$x^{3}+4x^{2}+16x-32x-64+2$$

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

$$x^{3}+4x^{2}-16x-64+2$$

Add -64 and 2 to get -62.

$$x^{3}+4x^{2}-16x-62$$