How do you multiply #4xy^2(3x^2-5xy+6y^2)#?

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Answer 1 · 2017-11-13T07:18:47

#12x^3y^2-20x^2y^3+24x^2y^4#

First, we need to know that
#a^n*a^m=a^(n+m)#

For this question, we can simply expand the bracket.
#4xy^2(3x^2-5xy+6y^2)#

#=3x^2*4xy^2-5xy*4xy^2+6y^2*4xy^2#

#=3*4*x^2*x*y^2-5*4*x*x*y*y^2+6*4*x^2*y^2*y^2#

#=12x^(2+1)y^2-20x^(1+1)y^(1+2)+24x^2y^(2+2)#

#=12x^3y^2-20x^2y^3+24x^2y^4#

Here is the answer :)