# What is the standard form of y= (-1/9x+3/2x^2)(3x-6) ?

Nov 1, 2017

$y = \frac{9}{2} {x}^{3} + 26 {x}^{2} - \frac{2}{3} x$
We foil and simplify.

#### Explanation:

This question will have the same process as any polynomial which multiplies two binomials. The only thing that makes people feel uncomfortable are the fractions! But no sweat...

Step 1: FOIL the binomials:
$\left(- \frac{1}{9} x + \frac{3}{2} {x}^{2}\right) \left(3 x - 6\right)$
$\left(- \frac{1}{9} x \times 3 x\right) + \left(- \frac{1}{9} x \times - 6\right) + \left(\frac{3}{2} {x}^{2} \times 3 x\right) + \left(\frac{3}{2} {x}^{2} \times - 6\right)$
$\left(- \frac{1}{3} {x}^{2}\right) + \left(- \frac{2}{3} x\right) + \left(\frac{9}{2} {x}^{3}\right) + \left(9 {x}^{2}\right)$

Step 2: Use the commutative property to rearrange the terms and combine the like terms:
$\frac{9}{2} {x}^{3} + \left(- \frac{1}{3} {x}^{2} + 9 {x}^{2}\right) + \left(- \frac{2}{3} x\right)$
$\frac{9}{2} {x}^{3} + \frac{26}{3} {x}^{2} + \left(- \frac{2}{3} x\right)$

Step 3: Drop the parentheses and simplify :) Pay attention to negatives!
$y = \frac{9}{2} {x}^{3} + \frac{26}{3} {x}^{2} - \frac{2}{3} x$