Question

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

Answer 1

`y=9/2x^3+26x^2-2/3x`
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:
`(-1/9x+3/2x^2)(3x-6)`
`(-1/9x times 3x)+(-1/9x times -6) + (3/2x^2 times 3x) + (3/2x^2 times -6)`
`(-1/3x^2)+(-2/3x)+(9/2x^3)+(9x^2)`

Step 2: Use the commutative property to rearrange the terms and combine the like terms:
`9/2x^3+(-1/3x^2+9x^2)+(-2/3x)`
`9/2x^3+26/3x^2+(-2/3x)`

Step 3: Drop the parentheses and simplify :) Pay attention to negatives!
`y=9/2x^3+26/3x^2-2/3x`