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

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

Evaluate

$$\left(x+2\right)\left(x\left(x+4\right)-4\right)$$

Solution Steps

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

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

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

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

Use the distributive property to multiply x by x^{2}+4x+4.

$$x^{3}+4x^{2}+4x+2\left(x+2\right)\left(x-2\right)$$

Use the distributive property to multiply 2 by x+2.

$$x^{3}+4x^{2}+4x+\left(2x+4\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 2x+4 by each term of x-2.

$$x^{3}+4x^{2}+4x+2x^{2}-4x+4x-8$$

Combine -4x and 4x to get 0.

$$x^{3}+4x^{2}+4x+2x^{2}-8$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$x^{3}+6x^{2}+4x-8$$

Expand

$$x^{3}+6x^{2}+4x-8$$

Solution Steps

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

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

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

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

Use the distributive property to multiply x by x^{2}+4x+4.

$$x^{3}+4x^{2}+4x+2\left(x+2\right)\left(x-2\right)$$

Use the distributive property to multiply 2 by x+2.

$$x^{3}+4x^{2}+4x+\left(2x+4\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 2x+4 by each term of x-2.

$$x^{3}+4x^{2}+4x+2x^{2}-4x+4x-8$$

Combine -4x and 4x to get 0.

$$x^{3}+4x^{2}+4x+2x^{2}-8$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$x^{3}+6x^{2}+4x-8$$