Solve P(x)=(x^{3}-x)(x^3+8x)-x^2(x^4-6x^2)-1

$$P ( x ) = ( x ^ { 3 } - x ) ( x ^ { 3 } + 8 x ) - x ^ { 2 } ( x ^ { 4 } - 6 x ^ { 2 } ) - 1$$

Evaluate

$$13x^{4}-8x^{2}-1$$

Solution Steps

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

$$x^{6}+7x^{4}-8x^{2}-x^{2}\left(x^{4}-6x^{2}\right)-1$$

Use the distributive property to multiply x^{2} by x^{4}-6x^{2}.

$$x^{6}+7x^{4}-8x^{2}-\left(x^{6}-6x^{4}\right)-1$$

To find the opposite of x^{6}-6x^{4}, find the opposite of each term.

$$x^{6}+7x^{4}-8x^{2}-x^{6}+6x^{4}-1$$

Combine x^{6} and -x^{6} to get 0.

$$7x^{4}-8x^{2}+6x^{4}-1$$

Combine 7x^{4} and 6x^{4} to get 13x^{4}.

$$13x^{4}-8x^{2}-1$$

Expand

$$13x^{4}-8x^{2}-1$$

Solution Steps

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

$$x^{6}+7x^{4}-8x^{2}-x^{2}\left(x^{4}-6x^{2}\right)-1$$

Use the distributive property to multiply x^{2} by x^{4}-6x^{2}.

$$x^{6}+7x^{4}-8x^{2}-\left(x^{6}-6x^{4}\right)-1$$

To find the opposite of x^{6}-6x^{4}, find the opposite of each term.

$$x^{6}+7x^{4}-8x^{2}-x^{6}+6x^{4}-1$$

Combine x^{6} and -x^{6} to get 0.

$$7x^{4}-8x^{2}+6x^{4}-1$$

Combine 7x^{4} and 6x^{4} to get 13x^{4}.

$$13x^{4}-8x^{2}-1$$