# Thread: Help me figure out how to factor this.

1. ## Help me figure out how to factor this.

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

2. Originally Posted by bradycat
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.

3. Originally Posted by bradycat
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
1) $(a - b)^2 - 9 = (a - b)^2 - 3^2$

Use the Difference of Two Squares rule.

2) $a(x + y)^2 - a = a\left[(x + y)^2 - 1\right]$

$= a\left[(x + y)^2 - 1^2\right]$

Use the Difference of Two Squares rule.

3) $4x^2 - (y - 2z)^2 = (2x)^2 - (y - 2z)^2$.

Use the Difference of Two Squares rule.

4. ## To the Two who have replied

Hello,
Yes this is the Difference between two squares.
I thank you for your help and will go over them to understand.
Thank you for your help in this.
Joanne

5. ## OK to make sure I get this

So 7x^2y^4-28y^6
equals
7y^4(x^2-4y^2)
into
7y^4(x+2y)(x-2y)

Do I have this correct??
Thanks again
Joanne

6. ## Prove it?

Hiya,
In the 2nd one, was does it end in -1. I have gone thru it a few times and can't figure out why.
Can you explain please,thanks
Joanne

7. Originally Posted by bradycat
So 7x^2y^4-28y^6
equals
7y^4(x^2-4y^2)
into
7y^4(x+2y)(x-2y)

Do I have this correct??
Thanks again
Joanne
Seems perfect

8. Originally Posted by bradycat
Hiya,
In the 2nd one, was does it end in -1. I have gone thru it a few times and can't figure out why.
Can you explain please,thanks
Joanne
Because I have taken out a common factor of $a$.

$\frac{a(x + y)^2}{a} = (x + y)^2$

and

$\frac{-a}{a} = -1$.

9. Originally Posted by bradycat
Hiya,
In the 2nd one, was does it end in -1. I have gone thru it a few times and can't figure out why.
Can you explain please,thanks
Joanne
2)

hmmm in a simpler example..

x^2 -x = x(x-1)

does that make sense? the reason why there is a -1 term at the end is because when u factor (a) from (-a) you are left with a (-1)

10. ## Prove It & S31J41

Thank you for the help.
I understand now. It just want not clicking for some reason.
Have a good one.
Joanne

11. ## goodness!

Well her question is factoring as well but looks a lot harder than mine as I am not sure I understand all her problems lol...

I need to get a book I am guessing this is all covered in detail in a college Algebra book?

12. This is high-school algebra (like Year 8 or 9).

Just look up Difference of Two Squares in Google.

13. ## k

Keywords make a big difference in searching lol..

Found Difference of two squares - A complete course in algebra

pretty cool.