Solve x(x+2)^2-3(x+2)^2

$$x ( x + 2 ) ^ { 2 } - 3 ( x + 2 ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -3 by x^{2}+4x+4.

$$x^{3}+4x^{2}+4x-3x^{2}-12x-12$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$x^{3}+x^{2}+4x-12x-12$$

Combine 4x and -12x to get -8x.

$$x^{3}+x^{2}-8x-12$$

Expand

$$x^{3}+x^{2}-8x-12$$

Solution Steps

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

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

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

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

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

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

Use the distributive property to multiply -3 by x^{2}+4x+4.

$$x^{3}+4x^{2}+4x-3x^{2}-12x-12$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$x^{3}+x^{2}+4x-12x-12$$

Combine 4x and -12x to get -8x.

$$x^{3}+x^{2}-8x-12$$