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 $a^2-b^2=(a+b)(a-b)$

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

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

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

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

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

How do you factor 36 ( 2x-y)^2 - 25 (u-2y)^236 ( 2x-y)^2 - 25 (u-2y)^2?