Solve x^5(x-2)^3(x+7)

$$x ^ { 5 } ( x - 2 ) ^ { 3 } ( x + 7 )$$

Evaluate

$$\left(x+7\right)\left(x-2\right)^{3}x^{5}$$

Solution Steps

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

$$x^{5}\left(x^{3}-6x^{2}+12x-8\right)\left(x+7\right)$$

Use the distributive property to multiply x^{5} by x^{3}-6x^{2}+12x-8.

$$\left(x^{8}-6x^{7}+12x^{6}-8x^{5}\right)\left(x+7\right)$$

Use the distributive property to multiply x^{8}-6x^{7}+12x^{6}-8x^{5} by x+7 and combine like terms.

$$x^{9}+x^{8}-30x^{7}+76x^{6}-56x^{5}$$

Expand

$$x^{9}+x^{8}-30x^{7}+76x^{6}-56x^{5}$$

Solution Steps

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

$$x^{5}\left(x^{3}-6x^{2}+12x-8\right)\left(x+7\right)$$

Use the distributive property to multiply x^{5} by x^{3}-6x^{2}+12x-8.

$$\left(x^{8}-6x^{7}+12x^{6}-8x^{5}\right)\left(x+7\right)$$

Use the distributive property to multiply x^{8}-6x^{7}+12x^{6}-8x^{5} by x+7 and combine like terms.

$$x^{9}+x^{8}-30x^{7}+76x^{6}-56x^{5}$$