Solve (x+2)(x-8)^3(x-1)^2

$$( x + 2 ) ( x - 8 ) ^ { 3 } ( x - 1 ) ^ { 2 }$$

Evaluate

$$\left(x+2\right)\left(x-1\right)^{2}\left(x-8\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-8\right)^{3}.

$$\left(x+2\right)\left(x^{3}-24x^{2}+192x-512\right)\left(x-1\right)^{2}$$

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

$$\left(x+2\right)\left(x^{3}-24x^{2}+192x-512\right)\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply x+2 by x^{3}-24x^{2}+192x-512 and combine like terms.

$$\left(x^{4}-22x^{3}+144x^{2}-128x-1024\right)\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply x^{4}-22x^{3}+144x^{2}-128x-1024 by x^{2}-2x+1 and combine like terms.

$$x^{6}-24x^{5}+189x^{4}-438x^{3}-624x^{2}+1920x-1024$$

Expand

$$x^{6}-24x^{5}+189x^{4}-438x^{3}-624x^{2}+1920x-1024$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-8\right)^{3}.

$$\left(x+2\right)\left(x^{3}-24x^{2}+192x-512\right)\left(x-1\right)^{2}$$

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

$$\left(x+2\right)\left(x^{3}-24x^{2}+192x-512\right)\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply x+2 by x^{3}-24x^{2}+192x-512 and combine like terms.

$$\left(x^{4}-22x^{3}+144x^{2}-128x-1024\right)\left(x^{2}-2x+1\right)$$

Use the distributive property to multiply x^{4}-22x^{3}+144x^{2}-128x-1024 by x^{2}-2x+1 and combine like terms.

$$x^{6}-24x^{5}+189x^{4}-438x^{3}-624x^{2}+1920x-1024$$