# What is the standard form of y= (x - 5)^2(6-x)?

Dec 17, 2015

$y = - {x}^{3} + 16 {x}^{2} - 50 x + 150$

#### Explanation:

First expand ${\left(x - 5\right)}^{2}$.

${\left(x - 5\right)}^{2} = \left(x - 5\right) \left(x - 5\right) = {x}^{2} - 10 x + 25$

Now, you know that $y = \left({x}^{2} - 10 x + 25\right) \left(6 - x\right)$

Distribute again.

$y = 6 {x}^{2} - 60 x + 150 - {x}^{3} + 10 {x}^{2} - 25 x$

Combine like terms and write the terms in order of descending degree (biggest exponent first).

$y = - {x}^{3} + 16 {x}^{2} - 50 x + 150$