Solve y=(-x+1)(x+3)(x-1)

$$y = ( - x + 1 ) ( x + 3 ) ( x - 1 )$$

Solve for y

$$y=-\left(x+3\right)\left(x-1\right)^{2}$$

Solution Steps

Use the distributive property to multiply -x+1 by x+3.

$$y=\left(\left(-x\right)x+3\left(-x\right)+x+3\right)\left(x-1\right)$$

Use the distributive property to multiply \left(-x\right)x+3\left(-x\right)+x+3 by x-1 and combine like terms.

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

Multiply -3 and -1 to get 3.

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

Combine 3x and 2x to get 5x.

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

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

$$y=-x^{3}+2\left(-1\right)xx+5x+x^{2}-3$$

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

$$y=-x^{3}+2\left(-1\right)x^{2}+5x+x^{2}-3$$

Multiply 2 and -1 to get -2.

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

Combine -2x^{2} and x^{2} to get -x^{2}.

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