SOLUTION: How do I factor when either square is a square of a polynomial? Such as in this problem: 49a^2-(5a-4b)^2 Any help is appriciated. Micah

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I factor when either square is a square of a polynomial? Such as in this problem: 49a^2-(5a-4b)^2 Any help is appriciated. Micah      Log On


   

Question 262899: How do I factor when either square is a square of a polynomial?
Such as in this problem:
49a^2-(5a-4b)^2
Any help is appriciated.
Micah
Found 2 solutions by nerdybill, checkley77:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Think of it as the special condition of "difference of squares".
.
We could rewrite:
49a^2-(5a-4b)^2
as
(7a)^2-(5a-4b)^2
.
Now, we can factor as:
(7a - (5a-4b))(7a + (5a-4b))
.
(7a - 5a+4b)(7a + 5a-4b)
.
(2a+4b)(12a-4b)
2(a+2b)4(3a-b)
8(a+2b)(3a-b)

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
49a^2-(5a-4b)^2
[7a-(5a-4b)][7a+(5a-4b)
[7a-5a+4b][7a+5a-4b]
[2a+4b][12a-4b] ans.