Question

How do you factor `2x^2+7xy-15y^2`?

Answer 1

`color(magenta)(=(2x-3y)(x+5y)`

Explanation:

`2x^2+7xy-15y^2`

`=2x^2+10xy-3xy-15y^2`

`=2x(x+5y)-3y(x+5y)`

`color(magenta)(=(2x-3y)(x+5y)`

~Hope this helps! :)

Answer 2

`(x+5y)(2x-3y)`

Explanation:

`"factor using the a-c method"`

`"The factors of - 30 which sum to + 7 are + 10 and - 3"`

`rArr2x^2+10xy-3xy-15y^2larrcolor(blue)"split middle term"`

`=color(red)(2x)(x+5y)color(red)(-3y)(x+5y)larrcolor(blue)"factor by grouping"`

`=(x+5y)(color(red)(2x-3y))`

`rArr2x^2+7xy-15y^2=(x+5y)(2x-3y)`

Answer 3

`(x+5y)(2x-3y)`

Explanation:

`2x^2+7xy-15y^2 = 2x^2+10xy-3xy-15y^2`

`=2x(x+5y)-3y(x+5y)=(x+5y)(2x-3y)` [Ans]