How do you simplify #-2y^3(3x^2y - 6x^2y^2)#?

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Answer 1 · 2018-06-01T10:54:30

#-2y^3(3x^2y-6x^2y^2)=color(blue)(-6x^2y^4+12x^2y^5#

Simplify:

#-2y^3(3x^2y-6x^2y^2)#

Distribute #-2y^3#.

#(-2y^3*3x^2y)-(-2y^3*6x^2y^2)#

Simplify parentheses.

#-2y^3*3x^2y+2y^3*6x^2y^2#

Multiply constants.

#-6y^3*x^2y+12y^3*x^2y^2#

Group like variables.

#-6x^2y^3y+12x^2y^2y^3#

Apply product rule: #a^ma^n=a^(m+n)#

#-6x^2y^(3+1)+12x^2y^(2+3)#

Simplify.

#-6x^2y^4+12x^2y^5#

Answer 2 · 2018-06-01T10:55:22

#-6x^2y^2+12x^2y^3#

Expanding we get
#-6x^2y^2+12x^2y^3#