Efficiently Factor Polynomials: Solving 36(2x-y)^2 - 25(u-2y)^2

[richievuong]

Factoring polynomials(2nd problem)

Factor:

36(2x-y)^2 - 25(u-2y)^2

Having trouble where to start...should I expand out?

 

[KyoPhan]

Factor:

36(2x-y)^2 - 25(u-2y)^2

Having trouble where to start...should I expand out?

Is that u and u, or is that suppose to be an x

 

[StatusX]

You can start by noticing that that is the difference of two squares.

 

[richievuong]

Yeah its a U, got it figured out now.

I have another one that I'm having trouble with:

(a^2 - ab)^2 -8b^2(a^2 - ab) + 12b^4

I tried factoring the a^2-ab out

= (a^2-ab)[-8b^2 + (a^2-ab)] + 12b^4

Tried a couple methods none really worked out...what should be my next step? Should i factor a^2-ab to a(a-b)?

 

[StatusX]

Do you know how to factor ax^2+bxy+cy^2? Because this expression is in that form.

 

[Random333]

Yeah its a U, got it figured out now.

I have another one that I'm having trouble with:

(a^2 - ab)^2 -8b^2(a^2 - ab) + 12b^4

I tried factoring the a^2-ab out

= (a^2-ab)[-8b^2 + (a^2-ab)] + 12b^4

Tried a couple methods none really worked out...what should be my next step? Should i factor a^2-ab to a(a-b)?

Make

(a^2 - ab)=X
AND
b^2=Y

Therefore, X^2-8xy+12y^2

Then solve and sub back in.