How do you factor the expressions #x^2-xy-2y^2#?

1 Answer
mason m
Mar 5, 2016

#(x+y)(x-2y)#

Explanation:

Look for a factor pair of the product of the coefficients of the first and last terms #1xx-2=-2# whose sum is the coefficient of the middle term, #-1#. The factors that work are #-2# and #1#.

Split up #-xy# into #-2xy# and #+xy# (their coefficients are the two factors we just found, #-2# and #1#) and then factor by grouping.

#=(x^2-2xy)+(xy-2y^2)#

#=x(x-2y)+y(x-2y)#

#=(x+y)(x-2y)#

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