11.05.2018: One Lesson of Math

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)

#ShaniaTwain