Question

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

Answer 1

`(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)`

Answer 2

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)`