Solve y=-x^2(x-3)(x+5)

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

Solve for y

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

Solution Steps

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

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

Multiply -3 and -1 to get 3.

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

Use the distributive property to multiply \left(-x^{2}\right)x+3x^{2} by x+5.

$$y=\left(-x^{2}\right)x^{2}+5\left(-x^{2}\right)x+3x^{3}+15x^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$y=-x^{4}+5\left(-1\right)x^{2}x+3x^{3}+15x^{2}$$

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

$$y=-x^{4}+5\left(-1\right)x^{3}+3x^{3}+15x^{2}$$

Multiply 5 and -1 to get -5.

$$y=-x^{4}-5x^{3}+3x^{3}+15x^{2}$$

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

$$y=-x^{4}-2x^{3}+15x^{2}$$