Solve x^3(x-1)+11x^2(x-1)-42x(x-1)

$$x ^ { 3 } ( x - 1 ) + 11 x ^ { 2 } ( x - 1 ) - 42 x ( x - 1 )$$

Evaluate

$$x\left(x-3\right)\left(x-1\right)\left(x+14\right)$$

Solution Steps

Use the distributive property to multiply x^{3} by x-1.

$$x^{4}-x^{3}+11x^{2}\left(x-1\right)-42x\left(x-1\right)$$

Use the distributive property to multiply 11x^{2} by x-1.

$$x^{4}-x^{3}+11x^{3}-11x^{2}-42x\left(x-1\right)$$

Combine -x^{3} and 11x^{3} to get 10x^{3}.

$$x^{4}+10x^{3}-11x^{2}-42x\left(x-1\right)$$

Use the distributive property to multiply -42x by x-1.

$$x^{4}+10x^{3}-11x^{2}-42x^{2}+42x$$

Combine -11x^{2} and -42x^{2} to get -53x^{2}.

$$x^{4}+10x^{3}-53x^{2}+42x$$

Expand

$$x^{4}+10x^{3}-53x^{2}+42x$$

Solution Steps

Use the distributive property to multiply x^{3} by x-1.

$$x^{4}-x^{3}+11x^{2}\left(x-1\right)-42x\left(x-1\right)$$

Use the distributive property to multiply 11x^{2} by x-1.

$$x^{4}-x^{3}+11x^{3}-11x^{2}-42x\left(x-1\right)$$

Combine -x^{3} and 11x^{3} to get 10x^{3}.

$$x^{4}+10x^{3}-11x^{2}-42x\left(x-1\right)$$

Use the distributive property to multiply -42x by x-1.

$$x^{4}+10x^{3}-11x^{2}-42x^{2}+42x$$

Combine -11x^{2} and -42x^{2} to get -53x^{2}.

$$x^{4}+10x^{3}-53x^{2}+42x$$