Solve 2x^2(x+1)^2-12x(x+1)=

$$2 x ^ { 2 } ( x + 1 ) ^ { 2 } - 12 x ( x + 1 ) =$$

Evaluate

$$2x\left(x-2\right)\left(x+1\right)\left(x+3\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$2x^{2}\left(x^{2}+2x+1\right)-12x\left(x+1\right)$$

Use the distributive property to multiply 2x^{2} by x^{2}+2x+1.

$$2x^{4}+4x^{3}+2x^{2}-12x\left(x+1\right)$$

Use the distributive property to multiply -12x by x+1.

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

Combine 2x^{2} and -12x^{2} to get -10x^{2}.

$$2x^{4}+4x^{3}-10x^{2}-12x$$

Expand

$$2x^{4}+4x^{3}-10x^{2}-12x$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$2x^{2}\left(x^{2}+2x+1\right)-12x\left(x+1\right)$$

Use the distributive property to multiply 2x^{2} by x^{2}+2x+1.

$$2x^{4}+4x^{3}+2x^{2}-12x\left(x+1\right)$$

Use the distributive property to multiply -12x by x+1.

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

Combine 2x^{2} and -12x^{2} to get -10x^{2}.

$$2x^{4}+4x^{3}-10x^{2}-12x$$