(2m%5E2-3m%2B2).jpeg "(6m-2)(2m^2-3m+2)")
Multiplying Polynomials: (6m-2)(2m^2-3m+2)
This article will guide you through the process of multiplying the polynomials (6m-2)(2m^2-3m+2).
Understanding the Problem
We are given two polynomials:
- (6m-2) which is a binomial (two terms)
- (2m^2-3m+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 (6m-2) by each term of the second polynomial (2m^2-3m+2).
Step-by-Step 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 (6m-2)(2m^2-3m+2) is 12m^3 - 22m^2 + 18m - 4.