Multiply the following: (X-3Y) (X^2 + 3XY + 9Y^2)

[lotus]

Original problem: (X-3Y) (X^2 + 3XY + 9Y^2)

My work so far: Step 1: =X (X^2 +3XY + 9Y^2) -3Y(X^2 + 3XY + 9Y^2)

Step 2: =X^3 + 3X^2 Y + 9XY^2 - 3X^2 Y - 9XY^2 - 27Y^3

I'm confused as to what to do next, please help.

 

[MarkFL]

Original problem: (X-3Y) (X^2 + 3XY + 9Y^2)

My work so far: Step 1: =X (X^2 +3XY + 9Y^2) -3Y(X^2 + 3XY + 9Y^2)

Step 2: =X^3 + 3X^2 Y + 9XY^2 - 3X^2 Y - 9XY^2 - 27Y^3

I'm confused as to what to do next, please help.

Hello and welcome to FMH! :cool:

What you've done so far is good...now what you want to do is combine any like terms, that is terms that have the same exponent on X and Y simultaneously. For example, the terms:

\(\displaystyle 3x^2y^6\)

and

\(\displaystyle 7x^2y^6\)

are like terms because the exponents on all variables are the same, and if we were to sum them, we would be able to write:

\(\displaystyle 3x^2y^6+7x^2y^6=10x^2y^6\)

Do you find any terms you can combine?