How do you factor by grouping. 4+5xy-10y-2x4+5xy10y2x?

1 Answer
Mar 12, 2018

(2-x)(2-5y)(2x)(25y)

Explanation:

If you have four terms without a common factor you need to group them.

Grouping like this (4+5xy)+(-10y-2x)(4+5xy)+(10y2x) achieves little.

Group the terms differently:

(4-2x)+(5xy-10y)" "larr(42x)+(5xy10y) find the HCF of each bracket

=2(2-x) color(blue)(+5y(x-2))" "larr=2(2x)+5y(x2) divide -11 out as a factor

=2(2-x)-5y(-x+2)" "larr=2(2x)5y(x+2) the signs change

2(2-x)-5y(2-x)" "larr2(2x)5y(2x) makes equal brackets

(2-x)(2-5y)" "larr(2x)(25y) there are two factor

OR:

(4-10y) +(-2x+5xy)(410y)+(2x+5xy)

=2(2-5y)+x(-2+5y)=2(25y)+x(2+5y)

=2(2-5y)-x(2-5y)=2(25y)x(25y)

=(2-5y)(2-x)=(25y)(2x)