Factor out the greatest common factor from each polynomial. See Example 1. 2(a+b)+4m(a+b)

Verified step by step guidance

1. Identify the terms in the expression: \$2(a+b)\( and \)4m(a+b)$.
2. Look for the greatest common factor (GCF) shared by both terms. Notice that both terms contain the binomial factor \((a+b)\).
3. Also, consider the numerical coefficients: 2 and 4. The GCF of 2 and 4 is 2.
4. Combine the GCF of the coefficients and the common binomial factor to get the overall GCF: \$2(a+b)$.
5. Factor out \$2(a+b)\( from each term, rewriting the expression as \)2(a+b)(1 + 2m)$.

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest expression that divides each term of a polynomial without leaving a remainder. Identifying the GCF helps simplify polynomials by factoring out common numerical coefficients and variable expressions shared by all terms.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and solves equations by breaking down complex polynomials into simpler multiplicative components.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It is used in reverse during factoring to extract the common factor from terms, transforming a sum into a product, which is essential for factoring out the GCF.