factor 4x2-25y2z2

Question

factor 4x2-25y2z2

mathstudent55 · Answer

Look at thye pattern:
$a^2 - b^2 = (a + b)(a - b) $

mathstudent55 · Answer

If you have a binomial (two terms) with one term being subtracted from the other. The first term is the square of something and the second term is also the square of something. Then the factoring is a product of a sum and a difference of the terms without the squares.

anonymous · Answer

so would it be (2x+5yx)(2x-5yz)

agent0smith · Answer

$$\Large 4x^2-25y^2z^2 = (2x)^2 - (5yz)^2$$

agent0smith · Answer

Yes, but you have a z where an x should be.

agent0smith · Answer

I mean, an x where a z should be. Prob a typo.

anonymous · Answer

okay so (2x+5yz)(2x-5yz)

mathstudent55 · Answer

Let's look at this example.
You have two terms.
The second term is being subtracted from the first term.
The first term is $4x^2$, the square of $2x$.
The second term is $25y^2z^2$ which is the square of $5yz$.
Since all our conditions are met, then
$4x^2 - 25y^2z^2 = (2x + 5yz)(2x - 5yz) $

anonymous · Answer

thanks everyone for your help