Solve y=-(x^3+4)(5x-6)(x-7)

$$y = - ( x ^ { 3 } + 4 ) ( 5 x - 6 ) ( x - 7 )$$

Solve for y

$$y=-\left(x-7\right)\left(5x-6\right)\left(x^{3}+4\right)$$

Solution Steps

To find the opposite of x^{3}+4, find the opposite of each term.

$$y=\left(-x^{3}-4\right)\left(5x-6\right)\left(x-7\right)$$

Use the distributive property to multiply -x^{3}-4 by 5x-6.

$$y=\left(-5x^{4}+6x^{3}-20x+24\right)\left(x-7\right)$$

Use the distributive property to multiply -5x^{4}+6x^{3}-20x+24 by x-7 and combine like terms.

$$y=-5x^{5}+41x^{4}-42x^{3}-20x^{2}+164x-168$$