Solve x(x-1)(x+1)(-x^2+5x+6)

$$x ( x - 1 ) ( x + 1 ) ( - x ^ { 2 } + 5 x + 6 )$$

Evaluate

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

Solution Steps

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

$$\left(x^{2}-x\right)\left(x+1\right)\left(-x^{2}+5x+6\right)$$

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

$$\left(x^{3}-x\right)\left(-x^{2}+5x+6\right)$$

Use the distributive property to multiply x^{3}-x by -x^{2}+5x+6.

$$x^{3}\left(-x^{2}\right)+5x^{4}+6x^{3}-x\left(-x^{2}\right)-5x^{2}-6x$$

Multiply -1 and -1 to get 1.

$$x^{3}\left(-x^{2}\right)+5x^{4}+6x^{3}+xx^{2}-5x^{2}-6x$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}\left(-x^{2}\right)+5x^{4}+6x^{3}+x^{3}-5x^{2}-6x$$

Combine 6x^{3} and x^{3} to get 7x^{3}.

$$x^{3}\left(-x^{2}\right)+5x^{4}+7x^{3}-5x^{2}-6x$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$x^{5}\left(-1\right)+5x^{4}+7x^{3}-5x^{2}-6x$$

Expand

$$-x^{5}+5x^{4}+7x^{3}-5x^{2}-6x$$

Solution Steps

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

$$\left(x^{2}-x\right)\left(x+1\right)\left(-x^{2}+5x+6\right)$$

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

$$\left(x^{3}-x\right)\left(-x^{2}+5x+6\right)$$

Use the distributive property to multiply x^{3}-x by -x^{2}+5x+6.

$$x^{3}\left(-x^{2}\right)+5x^{4}+6x^{3}-x\left(-x^{2}\right)-5x^{2}-6x$$

Multiply -1 and -1 to get 1.

$$x^{3}\left(-x^{2}\right)+5x^{4}+6x^{3}+xx^{2}-5x^{2}-6x$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}\left(-x^{2}\right)+5x^{4}+6x^{3}+x^{3}-5x^{2}-6x$$

Combine 6x^{3} and x^{3} to get 7x^{3}.

$$x^{3}\left(-x^{2}\right)+5x^{4}+7x^{3}-5x^{2}-6x$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$x^{5}\left(-1\right)+5x^{4}+7x^{3}-5x^{2}-6x$$