Solve y=-x(x-2)(x-3)

$$y = - x ( x - 2 ) ( x - 3 )$$

Solve for y

$$y=-x\left(x-3\right)\left(x-2\right)$$

Solution Steps

Use the distributive property to multiply -x by x-2.

$$y=\left(\left(-x\right)x-2\left(-x\right)\right)\left(x-3\right)$$

Multiply -2 and -1 to get 2.

$$y=\left(\left(-x\right)x+2x\right)\left(x-3\right)$$

Use the distributive property to multiply \left(-x\right)x+2x by x-3.

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

Multiply -3 and -1 to get 3.

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

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

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

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

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

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

$$y=-x^{3}+5x^{2}-6x$$