Solve (x+1)(x-5)^3

$$( x + 1 ) ( x - 5 ) ^ { 3 }$$

Expand

$$x^{4}-14x^{3}+60x^{2}-50x-125$$

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}.

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

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

$$x^{4}-14x^{3}+60x^{2}-50x-125$$

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}.

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

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

$$x^{4}-14x^{3}+60x^{2}-50x-125$$