Factor this problem?

Question

Factor:

4xsquared - 25

Answer 1

Above answer is wrong. The correct answer is (2x+5)(2x-5).

The working is:

4xsquared -25 ==>(2x)^2 - 5^2 ===> As (a^2-b^2)=(a+b)(a-b)

==> (2x+5)(2x-5)

Answer 2

4x^2-25

In this problem, we would use difference of squares:
If we have a^2-b^2, that would factor to
(a-b)(a+b)

So in 4x^2-25 we have
2x^2-5^2

Then we can factor it into

(2x-5)(2x+5)

CHECK:

Use the FOIL method

F irsts
O utsides
I nsides
L asts

So, in (2x-5)(2x+5) we would FOIL it.

First, we do 2x * 2x, which is 4x^2. Then 2x * 5, which is 10x. Then -5 * 2x, which is -10x, and last, -5 * 5, or -25.

We now have

4x^2+10x-10x-25
The 10x and -10x cancel each other out so we are left with

4x^2-25, our original question.
Hope it helps ;)

Answer 3

When factoring binomials like this, take the square of the first term and the square of the second term. One factor is the first minus the second, the other is the first plus the second.

4(x^2)...........square root = 2x
25.................square root = 5

so...
4(x^2) - 25......factored = (2x - 5)(2x + 5)

Answer 4

The key here is to realize that both terms are, in themselves, squares. That makes this just a fancy case of x^2 - y^2, which equals (x+y)*(x-y).

The answer is (2x + 5)*(2x - 5).

Hope that helps!

Answer 5

since a^2 - b^2 = (a+b)(a-b) for any a and b,

4x^2 - 25 = (2x)^2 - (5)^2 -> a=2x, b=5
= (2x+5)(2x-5)

Answer 6

4x² - 25 = (2x + 5)(2x - 5)
.

Answer 7

does it help to look at it this way???

4x^2 +0x -25

Answer 8

(2x + 5)(2x - 5)

Answer 9

(2x + 5) * (2x - 5)

Answer 10

(2x + 5)(2x - 5)