Hello,
I am doing home work, but stuck on a couple of questions.
(a-b)^2-9
a(x+y)^2-a
4x^2-(y-2z)^2
I figured my other questions, but have no encounted these before, need help solving please.
thanks
Joanne
Hmmm.... I am going to assume that this chapter is on factoring difference of perfect squares. Difference of perfect squares are in the form a^2 - b^2 and their factored form is (a-b)(a+b). So..
a^2 - b^2 = (a-b)(a+b)
This formula is sufficient to help you solve all the problems. The first one is pretty straight forward, it is already in the difference of square form. THe second problem has a common factor of (a) so you can factor that out first, and then it will be in a difference of square form. As for the third one, you need to realize that 4x^2 is a difference of square (it is (2x)^2) and (y-2z)^2 is also obviously a square.
1) $\displaystyle (a - b)^2 - 9 = (a - b)^2 - 3^2$
Use the Difference of Two Squares rule.
2) $\displaystyle a(x + y)^2 - a = a\left[(x + y)^2 - 1\right]$
$\displaystyle = a\left[(x + y)^2 - 1^2\right]$
Use the Difference of Two Squares rule.
3) $\displaystyle 4x^2 - (y - 2z)^2 = (2x)^2 - (y - 2z)^2$.
Use the Difference of Two Squares rule.
Keywords make a big difference in searching lol..
Found Difference of two squares - A complete course in algebra
pretty cool.