How to Simplify #y^2-6xy+5x^2# ?

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Answer 1 · 2018-05-09T08:45:28

Assuming you mean 'factorise'.

#(y-x)(y-5x)#

Note that #(-1)xx(-5) = +5 color(white)("ddd")andcolor(white)("ddd") -1-5=-6#

The only way we can have #y^2# as the first term is to use:
#(y+?)(y+?)#

Using whole numbers, the only way we can have the last term as #+5x^2# is to use #1x xx5x# which means the construct could be:

#(y-1x)(y-5x)color(white)("ddd")->color(white)("ddd")(y-x)(y-5x)#

#color(blue)("Check")#

#+y(y-5x) -> y^2-5xy#
#-x(y-5x)-> ul(color(white)(y^2)-xy+5x^2 larr" Add")#
#color(white)("ddddddddddd.")y^2-6xy+5x^2color(white)("d")# as required