Solve y=-(x+12)(x+6)(x-6)+80

$$y = - ( x + 12 ) ( x + 6 ) ( x - 6 ) + 80$$

Solve for y

$$y=-\left(x+12\right)\left(x^{2}-36\right)+80$$

Solution Steps

To find the opposite of x+12, find the opposite of each term.

$$y=\left(-x-12\right)\left(x+6\right)\left(x-6\right)+80$$

Use the distributive property to multiply -x-12 by x+6 and combine like terms.

$$y=\left(-x^{2}-18x-72\right)\left(x-6\right)+80$$

Use the distributive property to multiply -x^{2}-18x-72 by x-6 and combine like terms.

$$y=-x^{3}-12x^{2}+36x+432+80$$

Add 432 and 80 to get 512.

$$y=-x^{3}-12x^{2}+36x+512$$