Solve left(x-2right)^3(x-6)

$${ \left(x-2 \right) }^{ 3 } (x-6)$$

Evaluate

$$\left(x-6\right)\left(x-2\right)^{3}$$

Solution Steps

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

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

Use the distributive property to multiply x^{3}-6x^{2}+12x-8 by x-6 and combine like terms.

$$x^{4}-12x^{3}+48x^{2}-80x+48$$

Expand

$$x^{4}-12x^{3}+48x^{2}-80x+48$$

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}.

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

Use the distributive property to multiply x^{3}-6x^{2}+12x-8 by x-6 and combine like terms.

$$x^{4}-12x^{3}+48x^{2}-80x+48$$