# What is the standard form of y=(3-x)(5x^2-2x)?

Jan 1, 2016

$y = - 5 {x}^{3} + 17 {x}^{2} - 6 x$

#### Explanation:

We just have to multiply the numbers inside the parenthesis. First, the first number in the first parenthesis multiplied by each number in the second one:
$3 \cdot 5 {x}^{2} + 3 \cdot \left(- 2 x\right) = 15 {x}^{2} - 6 x$

And now, the same thing: the second number in the first parenthesis multiplied by each number in the second one:
$\left(- x\right) \cdot 5 {x}^{2} + \left(- x\right) \cdot \left(- 2 x\right) = - 5 {x}^{3} + 2 {x}^{2}$

Then, we just put them together and order them in the cubic function standard form($y = A {x}^{3} + B {x}^{2} + C x + D$):
$y = 15 {x}^{2} - 6 x + - 5 {x}^{3} + 2 {x}^{2}$
$y = - 5 {x}^{3} + 17 {x}^{2} - 6 x$