Solve y=(x-3)^2(x-10)-9

$$y = ( x - 3 ) ^ { 2 } ( x - 10 ) - 9$$

Solve for y

$$y=-\left(-\left(x-10\right)\left(x-3\right)^{2}+9\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$y=\left(x^{2}-6x+9\right)\left(x-10\right)-9$$

Use the distributive property to multiply x^{2}-6x+9 by x-10 and combine like terms.

$$y=x^{3}-16x^{2}+69x-90-9$$

Subtract 9 from -90 to get -99.

$$y=x^{3}-16x^{2}+69x-99$$