Question

How do you factor `45x^2-20m^2`?

Answer 1

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

Explanation:

`"take out a "color(blue)"common factor "5`

`=5(9x^2-4m^2)`

`9x^2-4m^2" is a "color(blue)"difference of squares"`

`"which in general factors as"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"note that "(3x)^2=9x^2" and "(2m)^2=4m^2`

`"thus "a=3x" and "b=2m`

`rArr9x^2-4m^2=(3x-2m)(3x+2m)`

`rArr45x^2-20m^2=5(3x-2m)(3x+2m)`