How do you factor #36 ( 2x-y)^2 - 25 (u-2y)^2#?

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Answer 1 · 2016-04-22T07:14:49

#36(2x-y)^2-25(u-2y)^2#

= #(12x+5u-16y)(12x-5u+4y)#

As #36(2x-y)^2-25(u-2y)^2# is of the form #a^2-b^2# and #a^2-b^2=(a+b)(a-b)#

#36(2x-y)^2-25(u-2y)^2=6^2(2x-y)^2-5^2(u-2y)^2#

= #(6(2x-y))^2-(5(u-2y))^2#

= #[6(2x-y)+5(u-2y)]xx[6(2x-y)-5(u-2y)]#

= #[12x-6y+5u-10y]xx[12x-6y-5u+10y]#

= #[12x+5u-16y]xx[12x-5u+4y]#