Today's soundtrack is Shania Twain: Up (Red Disc).
This afternoon, I'm finishing up my homework from unit 3.1, which covered factoring. I spoke with my teacher about the problems that were giving me trouble and found that I need to substitute variables into the equations like this:
Factor 9(x-3)² - 4(2y+1)²
Right away, I'm going to substitute the expressions inside brackets for variables.
Let x-3 = a; let 2y+1 = b
9a² - 4b²
I recognize that this is a difference of squares:
(3a - 2b)(3a + 2b)
Now, I remove the variables and replace them with their original expressions:
[3(x-3)-2(2y+1)] [3(x-3)+2(2y+1)
I use distributive properties to multiply the terms:
(3x-9-4y-2)(3x-9+4y+2)
Finally, I combine like terms to get my answer:
(3x-4-11)(3x+4y-7)