Answer:
[tex]-12m^3n^4 + 48m^2n^5-24m^2n^3+28mn^5[/tex]
Step-by-step explanation:
Product to be determined is
[tex]-4mn^3*(-3m^2n+12mn^2-6m+7n^2)[/tex]
1. Distribute the parenthesis by multiplying each term inside the parenthesis by the monomial
[tex]= 4mn^3 (-3m^2n) + 4mn^3 \cdot 12mn^2 +4mn^3(-6m) + mn^3 \cdot 7n^2\\[/tex]
When multiplying two terms with leading constant coefficients and exponent powers of variables the following rules apply
- the constant coefficients multiply as normal
- any product [tex]m^a \cdot m^b = m^{a+b}[/tex]
Using these rules, each of the individual products work out as follows:
[tex]4mn^3 (-3m^2n) = -12m^3n^4\\\\4mn^3 \cdot 12mn^2 = 48m^2n^5\\\\4mn^3(-6m) = -24m^2n^3\\\\4mn^3 \cdot 7n^2 = 28mn^5\\\\[/tex]
The product is
[tex]-12m^3n^4 + 48m^2n^5-24m^2n^3+28mn^5[/tex]
