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

Aug 4, 2015

=color(blue)(-2x^2y^4+ 4xy^5

#### Explanation:

−color(blue)(y^3)(2x^2y−4xy^2)

Here, color(blue)(y^3 needs to be multiplied with both terms within the bracket.

=(−color(blue)(y^3))(2x^2y) −(−color(blue)(y^3))(4xy^2)

=-2x^2y*color(blue)(y^3) + 4xy^2*color(blue)(y^3

• As per property color(blue)(a^m*a^n=a^(m+n)

Applying the same to the exponents of $y$:

$= - 2 {x}^{2} {y}^{\textcolor{b l u e}{\left(3 + 1\right)}} + 4 x {y}^{\textcolor{b l u e}{\left(2 + 3\right)}}$

=color(blue)(-2x^2y^4+ 4xy^5