richievuong said:Factor:
36(2x-y)^2 - 25(u-2y)^2
Having trouble where to start...should I expand out?
Makerichievuong said: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)?
The purpose of factoring polynomials is to simplify and solve mathematical expressions by breaking them down into smaller, equivalent parts.
To efficiently factor polynomials, you can use various techniques such as grouping, factoring by grouping, the difference of squares formula, and the quadratic formula.
The first step is to factor out the greatest common factor, which in this case is 36. This leaves us with 36[(2x-y)^2 - (u-2y)^2]. Next, we can use the difference of squares formula to factor the expression within the parentheses. This gives us 36[(2x-y+u-2y)(2x-y-u+2y)]. Finally, we can simplify the expression to get the final factored form: 36[(2x-u)(x-3y)].
You can check if a polynomial is factored correctly by multiplying the factored form back together and comparing it to the original expression. The two should be equivalent.
Some common mistakes to avoid when factoring polynomials include forgetting to check for a common factor, not applying the correct factoring formula, and making errors when simplifying the factored expression.