Solve left(x-5right)^3(x-1)

$${ \left(x-5 \right) }^{ 3 } (x-1)$$

Evaluate

$$\left(x-1\right)\left(x-5\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-5\right)^{3}.

$$\left(x^{3}-15x^{2}+75x-125\right)\left(x-1\right)$$

Use the distributive property to multiply x^{3}-15x^{2}+75x-125 by x-1 and combine like terms.

$$x^{4}-16x^{3}+90x^{2}-200x+125$$

Expand

$$x^{4}-16x^{3}+90x^{2}-200x+125$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-5\right)^{3}.

$$\left(x^{3}-15x^{2}+75x-125\right)\left(x-1\right)$$

Use the distributive property to multiply x^{3}-15x^{2}+75x-125 by x-1 and combine like terms.

$$x^{4}-16x^{3}+90x^{2}-200x+125$$