How do you factor #8x^2 -10xy - 25y^2#?

2 Answers
May 30, 2018

#(4x+5y)(2x+5y)#

Explanation:

Let,
#a= 8, b= -10, c=-25#

When you multiply a and c together you get , -200

You then need to find two numbers that when you multiply them you get -200 and when you add them you get -10.

Those two numbers are, -20 and 10

From there,
#8x^2 -20xy+10xy-25y^2#

Break the expression into groups

#(8x^2 -20xy)+ (10xy-25y^2)#

Factorise further

#4x(2x+5y) +5y(2x+5y)#

#therefore 8x^2-10xy-25y^2 =(4x+5y)(2x+5y)#

May 30, 2018

The factors are #(2x-5y)(4x+5y)#

Explanation:

Find factors of #8 and 25# so that the products of the factors differ by #10#.

There is often some trial and error, but with practice you will get better at this.

#" "8 " "25#
#color(white)(..)darrcolor(white)(.)darr#
#" "2" "5" "rarr4xx5 = 20#
#" "4" "5" "rarr2xx5 = ul10#
#color(white)(xxxxxx.xxxxx.xxxx)10" "larr# difference is #10#

These are the correct factors, now find the correct signs.

The signs need to be different to give #-25 and -10#

#" "8 " "-25#
#color(white)(...)darrcolor(white)(.....)darr#
#" "2" "-5" "rarr4xx-5 = -20#
#" "4" "+5" "rarr2xx+5 = +ul10#
#color(white)(xxxxxxxxxxxxxxx.xxxx)-10" "larr# negative are greater

The factors are #(2x-5y)(4x+5y)#