Solve y=-x(x+4)(x+1)(x-4)

$$y=-x(x+4)(x+1)(x-4)$$

Solve for y

$$y=-x\left(x+1\right)\left(x^{2}-16\right)$$

Solution Steps

Use the distributive property to multiply -x by x+4.

$$y=\left(\left(-x\right)x+4\left(-x\right)\right)\left(x+1\right)\left(x-4\right)$$

Use the distributive property to multiply \left(-x\right)x+4\left(-x\right) by x+1 and combine like terms.

$$y=\left(\left(-x\right)x^{2}+5\left(-x\right)x+4\left(-x\right)\right)\left(x-4\right)$$

Use the distributive property to multiply \left(-x\right)x^{2}+5\left(-x\right)x+4\left(-x\right) by x-4 and combine like terms.

$$y=\left(-x\right)x^{3}+\left(-x\right)x^{2}-16\left(-x\right)x-16\left(-x\right)$$

Multiply -16 and -1 to get 16.

$$y=\left(-x\right)x^{3}+\left(-x\right)x^{2}+16xx-16\left(-x\right)$$

Multiply x and x to get x^{2}.

$$y=\left(-x\right)x^{3}+\left(-x\right)x^{2}+16x^{2}-16\left(-x\right)$$

Multiply -16 and -1 to get 16.

$$y=\left(-x\right)x^{3}+\left(-x\right)x^{2}+16x^{2}+16x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$y=-x^{4}-xx^{2}+16x^{2}+16x$$

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

$$y=-x^{4}-x^{3}+16x^{2}+16x$$