Multiplying Polynomials: (6m2)(2m^23m+2)
This article will guide you through the process of multiplying the polynomials (6m2)(2m^23m+2).
Understanding the Problem
We are given two polynomials:
 (6m2) which is a binomial (two terms)
 (2m^23m+2) which is a trinomial (three terms)
Our goal is to multiply these two polynomials together to obtain a new polynomial.
The Distributive Property
We will use the distributive property to multiply the polynomials. The distributive property states that to multiply a sum by a number, we multiply each term of the sum by that number:
a(b+c) = ab + ac
Applying this to our problem, we will multiply each term of the first polynomial (6m2) by each term of the second polynomial (2m^23m+2).
StepbyStep Solution

Multiply 6m by each term in the second polynomial:
 6m * 2m^2 = 12m^3
 6m * 3m = 18m^2
 6m * 2 = 12m

Multiply 2 by each term in the second polynomial:
 2 * 2m^2 = 4m^2
 2 * 3m = 6m
 2 * 2 = 4

Combine the results:
 12m^3  18m^2 + 12m  4m^2 + 6m  4

Simplify by combining like terms:
 12m^3  22m^2 + 18m  4
Final Answer
Therefore, the product of (6m2)(2m^23m+2) is 12m^3  22m^2 + 18m  4.