How do you multiply $3a^3b^2(-a^3b - a^2b^2)$ ?

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Answer 1 · 2015-08-21T07:17:58

$=color(blue)(-3a^5b^3(a-b)$

$color(blue)(3a^3b^2)(−a^3b−a^2b^2)$

$=(color(blue)(3a^3b^2)) * (−a^3b) + (color(blue)(3a^3b^2) ) *(−a^2b^2)$

$=-3a^3a^3b^2b −3a^3a^2b^2b^2$

By property $color(blue)(a^m*a^n = a^(m+n)$

Applying the same to exponents of $a$ and $b$

$=-3a^((3+3))b^((2+1)) −3a^((3+2))b^((2+2))$

$=-3a^6b^3 −3a^5b^4$

$=color(blue)(-3a^5b^3(a-b)$

How do you multiply 3a^3b^2(-a^3b - a^2b^2)3a^3b^2(-a^3b - a^2b^2)?