Solve y=x(x-13)^2(x+11)

$$y = x ( x - 13 ) ^ { 2 } ( x + 11 )$$

Solve for y

$$y=x\left(x+11\right)\left(x-13\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-13\right)^{2}.

$$y=x\left(x^{2}-26x+169\right)\left(x+11\right)$$

Use the distributive property to multiply x by x^{2}-26x+169.

$$y=\left(x^{3}-26x^{2}+169x\right)\left(x+11\right)$$

Use the distributive property to multiply x^{3}-26x^{2}+169x by x+11 and combine like terms.

$$y=x^{4}-15x^{3}-117x^{2}+1859x$$