How do you factor #25x^2-9y^2z^2#?
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As the difference between two squares.
# 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)#
Please see the steps and process of factorization below...
#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"!#
