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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply x^{2}+2x+1 by x-2 and combine like terms.

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

Use the distributive property to multiply x^{3}-3x-2 by x+3 and combine like terms.

$$x^{4}+3x^{3}-3x^{2}-11x-6$$

Expand

$$x^{4}+3x^{3}-3x^{2}-11x-6$$

Solution Steps

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

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

Use the distributive property to multiply x^{2}+2x+1 by x-2 and combine like terms.

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

Use the distributive property to multiply x^{3}-3x-2 by x+3 and combine like terms.

$$x^{4}+3x^{3}-3x^{2}-11x-6$$