Solve (x-1)x^2(x^2+11x+21)

$$( x - 1 ) x ^ { 2 } ( x ^ { 2 } + 11 x + 21 )$$

Expand

$$x^{5}+10x^{4}+10x^{3}-21x^{2}$$

Solution Steps

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

$$\left(x^{3}-x^{2}\right)\left(x^{2}+11x+21\right)$$

Use the distributive property to multiply x^{3}-x^{2} by x^{2}+11x+21 and combine like terms.

$$x^{5}+10x^{4}+10x^{3}-21x^{2}$$

Evaluate

$$\left(x-1\right)x^{2}\left(x^{2}+11x+21\right)$$

Solution Steps

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

$$\left(x^{3}-x^{2}\right)\left(x^{2}+11x+21\right)$$

Use the distributive property to multiply x^{3}-x^{2} by x^{2}+11x+21 and combine like terms.

$$x^{5}+10x^{4}+10x^{3}-21x^{2}$$