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

2 Answers
David Drayer · Zack M.
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)#

Jumbotron
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"!#

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