What is the standard form of y= (-1/9x+3/2x^2)(3x-6) y=(−19x+32x2)(3x−6)?

1 Answer
Angel R.
Nov 1, 2017

y=9/2x^3+26x^2-2/3xy=92x3+26x2−23x
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)(−19x+32x2)(3x−6)
(-1/9x times 3x)+(-1/9x times -6) + (3/2x^2 times 3x) + (3/2x^2 times -6)(−19x×3x)+(−19x×−6)+(32x2×3x)+(32x2×−6)
(-1/3x^2)+(-2/3x)+(9/2x^3)+(9x^2)(−13x2)+(−23x)+(92x3)+(9x2)

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)92x3+(−13x2+9x2)+(−23x)
9/2x^3+26/3x^2+(-2/3x)92x3+263x2+(−23x)

Step 3: Drop the parentheses and simplify :) Pay attention to negatives!
y=9/2x^3+26/3x^2-2/3xy=92x3+263x2−23x

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