Answer:
The product of polynomial [tex](-2m^3+3m^2-m)(4m^2+m-5)[/tex] is [tex]\mathbf{-8m^5+10m^4+9m^3-16m^2+5m}[/tex]
Step-by-step explanation:
We need to find the standard form of polynomial that represents the product of [tex](-2m^3+3m^2-m)(4m^2+m-5)[/tex]
Finding the product of polynomial
[tex](-2m^3+3m^2-m)(4m^2+m-5)\\=-2m^3(4m^2+m-5)+3m^2(4m^2+m-5)-m(4m^2+m-5)\\=-8m^5-2m^4+10m^3+12m^4+3m^3-15m^2-4m^3-m^2+5m\\Combining\:like\:terms\\=-8m^5-2m^4+12m^4+10m^3+3m^3-4m^3-15m^2-m^2+5m\\=-8m^5+10m^4+9m^3-16m^2+5m\\[/tex]
So, the product of polynomial [tex](-2m^3+3m^2-m)(4m^2+m-5)[/tex] is [tex]\mathbf{-8m^5+10m^4+9m^3-16m^2+5m}[/tex]
