Question

Factor Completely:
x^2 - (y - 6)^2

Answer 1

Notice that this is a difference of 2 squares. In general, \[x^2-a^2=(x-a)(x+a)\]Here, you have \(a=y-6\). Can you tell me what the factorization is now?

Answer 2

what???

Answer 3

where are you getting the a from?

Answer 4

The \(a\) is just some random variable I used.

Since \(x^2-a^2=(x-a)(x+a)\), and \(a=y-6\) using a simple substitution you get that \[x^2-(y-6)^2=(x-(y-6))(x+(y-6))\]

Answer 5

oooooohhhhh okay I get it!

Answer 6

:)

Answer 7

thank you!

Answer 8

You're welcome.