Solve (x+1)^3-3x(x+1)^2+x(2x^2+3x)

$$( x + 1 ) ^ { 3 } - 3 x ( x + 1 ) ^ { 2 } + x ( 2 x ^ { 2 } + 3 x )$$

Evaluate

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Solution Steps

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

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

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

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

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

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

Use the distributive property to multiply -3x by x^{2}+2x+1.

$$x^{3}+3x^{2}+3x+1-3x^{3}-6x^{2}-3x+2x^{3}+3x^{2}$$

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

$$-2x^{3}+3x^{2}+3x+1-6x^{2}-3x+2x^{3}+3x^{2}$$

Combine 3x^{2} and -6x^{2} to get -3x^{2}.

$$-2x^{3}-3x^{2}+3x+1-3x+2x^{3}+3x^{2}$$

Combine 3x and -3x to get 0.

$$-2x^{3}-3x^{2}+1+2x^{3}+3x^{2}$$

Combine -2x^{3} and 2x^{3} to get 0.

$$-3x^{2}+1+3x^{2}$$

Combine -3x^{2} and 3x^{2} to get 0.

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Factor

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