SOLUTION: factor: 4x(squared)-49y(squared) factor: 4x(squared)-28x+49 simplify the rational expression 1 ___________ _______ 1 + 1 ___ ____ r x

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Question 131488: factor:
4x(squared)-49y(squared)
factor:
4x(squared)-28x+49
simplify the rational expression
1
___________________
1 + 1
___ ____
r x
Found 2 solutions by 067isa, Earlsdon:
Answer by 067isa(13) About Me  (Show Source):
You can put this solution on YOUR website!
Factor
4X^2- 49Y^2= different between two sequares.
(2x-7y)(2x+7y)
4x^2-28x+49 (AC method is the fastest)
AC= (4)(49)= 196
so now we looking for two number that the sum will br 28 and the prdouct will be 28
here is all the factors that we can get 196
1.196
2.98
4.49
7.28
14.14
from all of theses which one the sum will be 28 is this case it will be the last one 14+14=28
4x^2-14x-14x+49 ( we used the Ac to do the grouping now)
2x(2x-7)-7(2X-7)= (2x-7)(2x-7)
OR another way to solve this is by it's a perfect sequare trinomail



Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
4x%5E2-49y%5E2 This is the difference of two squares:
%282x%29%5E2-%287y%29%5E2
The difference of two squares is factored like this:
A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29 Apply this toyour problem:
%282x%29%5E2-%287y%29%5E2+=+%282x%2B7y%29%282x-7y%29
---------------------------------
Factor:
4x%5E2-28x%2B49 Since the first and last terms are perfect squares: 4x%5E2+=+%282x%29%5E2 and 49+=+7%5E2, also, twice 2(7) = 28, the middle term of your equation, try:
4x%5E2-28x%2B49+=+%282x-7%29%282x-7%29 = %282x-7%29%5E2