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

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

Solve for y

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

Solution Steps

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

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

Multiply -1 and -1 to get 1.

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

Use the distributive property to multiply \left(-x\right)x+x by x-4.

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

Multiply -4 and -1 to get 4.

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

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

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

Combine 4x^{2} and x^{2} to get 5x^{2}.

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

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

$$y=-x^{3}+5x^{2}-4x$$