How do you multiply # (2x^2 + y^2)(x - 2y) #?

1 Answer
Jul 5, 2015

Answer:

By applying the distributive property several times you can get:
#(2x^2+y^2)(x-2y)#
#color(white)("XXXX")##= 2x^3+xy^2-4x^2y-2y^3#

Explanation:

The distributive property tells us that
#color(white)("XXXX")##(color(red)(a)+color(blue)(b))(color(green)(p)-color(orange)(q)) = (color(red)(a)+color(blue)(b))color(green)(p) - (color(red)(a)+color(blue)(b))color(orange)(q)#
and that
#color(white)("XXXX")##(color(red)(a)+color(blue)(b))color(green)(p) = color(red)(a)color(green)(p)+color(blue)(b)color(green)(p)#

Therefore
#color(white)("XXXX")##(color(red)(2x^2)+color(blue)(y^2))(color(green)(x)-color(orange)(2y))#

#color(white)("XXXX")##(color(red)(2x^2)+color(blue)(y^2))color(green)(x) - (color(red)(2x^2)+color(blue)(y^2))color(orange)(2y)#

#color(white)("XXXX")##=(color(red)(2x^2))(color(green)(x)) +(color(blue)(y^2))(color(green)(x)) - (color(red)(2x^2))(color(orange)(2y)) - (color(blue)(y^2))(color(orange)(2y))#

#color(white)("XXXX")##=2x^3+xy^2 -4x^2y-2y^3#