Solve x^2(x^2-1)-x(x^2-1)-6(x^2-1)

$$x ^ { 2 } ( x ^ { 2 } - 1 ) - x ( x ^ { 2 } - 1 ) - 6 ( x ^ { 2 } - 1 )$$

Evaluate

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

Solution Steps

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

$$x^{4}-x^{2}-x\left(x^{2}-1\right)-6\left(x^{2}-1\right)$$

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

$$x^{4}-x^{2}-\left(x^{3}-x\right)-6\left(x^{2}-1\right)$$

To find the opposite of x^{3}-x, find the opposite of each term.

$$x^{4}-x^{2}-x^{3}+x-6\left(x^{2}-1\right)$$

Use the distributive property to multiply -6 by x^{2}-1.

$$x^{4}-x^{2}-x^{3}+x-6x^{2}+6$$

Combine -x^{2} and -6x^{2} to get -7x^{2}.

$$x^{4}-7x^{2}-x^{3}+x+6$$

Expand

$$x^{4}-x^{3}-7x^{2}+x+6$$

Solution Steps

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

$$x^{4}-x^{2}-x\left(x^{2}-1\right)-6\left(x^{2}-1\right)$$

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

$$x^{4}-x^{2}-\left(x^{3}-x\right)-6\left(x^{2}-1\right)$$

To find the opposite of x^{3}-x, find the opposite of each term.

$$x^{4}-x^{2}-x^{3}+x-6\left(x^{2}-1\right)$$

Use the distributive property to multiply -6 by x^{2}-1.

$$x^{4}-x^{2}-x^{3}+x-6x^{2}+6$$

Combine -x^{2} and -6x^{2} to get -7x^{2}.

$$x^{4}-7x^{2}-x^{3}+x+6$$