Question

How do you factor `x^ { 2} + 5x y - 14y ^ { 2}`?

Answer 1

`(x-2y)(x+7y)`

Explanation:

Given:`" "x^2+5xy-14y^2`

Notice that `2xx7=14" and that "7-2 = +5`

`=>color(brown)(color(blue)((x-2y))(x+7y))`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Check by multiplying out the brackets")`

`color(brown)(color(blue)(x)(x+7y)color(blue)(-2y)(x+7y))`

`= x^2+7xy-2xy-14y^2`

`=x^2+5y-14y^2`