SOLUTION: I need help factoring the following: 16x^2-25

Question 104535: I need help factoring the following:
16x^2-25
Found 2 solutions by checkley75, TP:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
16X^2-25 FIND THE SQUARE ROOT OF BOTH INTEGERS. THE FACTORS ARE THE + & - OF THESE 2 FACTORS.
(4X+5)(4X-5)
Answer by TP(29) (Show Source): You can put this solution on YOUR website!
You need to know about the difference of two squares.
a^2 - b^2 = (a+b)*(a-b) or more simply,(a+b)(a-b).
In your question think of 16x^2 as (4^2)*x^2 or more simply,(4^2)(x^2).
Now (4^2)(x^2)=(4*x)^2 or more simply (4x)^2.
So 16x^2=(4x)^2.
Also think of 25 as (5)^2.
So now we can write: 16x^2-25=(4x)^2-(5)^2.
Now the difference of two squares tells us that
a^2-b^2=(a+b)(a-b).
Compare your (4x)^2-(5)^2 to a^2-b^2.
If you look carefully you can see that a is in the same place as 4x and b is in the same place as 5.
So now we can replace a and b by 4x and 5 respectively.
This means that
a^2-b^2=(a+b)(a-b) can be written as (4x)^2-(5)^2=(4x+5)(4x-5)ANS
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