How do you factor 25x^2-9y^2z^2?

2 Answers
Nov 28, 2017

As the difference between two squares.

Explanation:

25x^2 = ( 5x xx 5x)

9y^2z^2 = ( 3yz xx 3yz)

Rewrite this as

(5x - 3yz) xx ( 5x + 3yz)

Multiplying this out gives

25x^2 - 15 xyz + 15 xyz - 9y^2z^2

The - 15 xyz + 15xyz cancel each other out leaving

25x^2 - 9 y^2z^2 so the factors are

( 5x - 3yz) and (5x + 3yz)

Nov 28, 2017

Please see the steps and process of factorization below...

Explanation:

25x^2 - 9y^2 z^2

Using difference of two squares which means;

(a^2 - y^2) = (a + y) (a - y)

Hence applying the above question is similar there will be no difference..

25 = 5^2

x^2

9 = 3^2

y^2

z^2

We are all set!

25x^2 - 9y^2 z^2 = 5^2x^2 - 3^2 y^2 z^2

Applying the difference of two squares we will have;

(5x + 3yz) (5x - 3yz)

color(red)("Proof")

If we try to expand the above we will still have the question asked!

(5x + 3yz) (5x - 3yz)

5x (5x - 3yz) + 3yz (5x - 3yz)

25x^2 - 15xyz + 15xyz - 9y^2 z^2

25x^2 cancel(- 15xyz + 15xyz) - 9y^2 z^2

25x^2 - 9y^2 z^2

color(blue)"QED"!