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

1 Answer
Apr 15, 2018

Answer:

#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)#