How do you simplify #(a^3+2a^2b-ab^2+3b^3)(4ab)#?

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Answer 1 · 2015-08-21T07:25:29

#=color(blue)(4a^4b + 4a^3b^2 +12ab^4#

#(a^3+2a^2b−ab^2+3b^3)color(blue)((4ab)#

#=(a^3) * color(blue)((4ab)) +(2a^2b) * color(blue)((4ab)) - (ab^2) *color(blue)((4ab)) +(3b^3) .color(blue)((4ab)#

#=4a^3*ab + 8a^2b*ab - 4ab^2*ab +12b^3*ab#

By property
#color(blue)(a^m*a^n=a^(m+n)#
Applying the same to powers of #a# and #b#

#=4a^((3+1))b + 8a^((2+1))b^((1+1)) - 4a^((1+1))b^((2+1)) +12ab^(3+1)#

#=4a^4b + color(blue)(8a^3b^2 - 4a^2b^3) +12ab^4#

#=color(blue)(4a^4b + 4a^3b^2 +12ab^4#