Factor out the greatest common factor from each polynomial. See Example 1. 6x(a+b)-4y(a+b)

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest integer or algebraic expression that divides two or more terms without leaving a remainder. To find the GCF, identify the common factors in the coefficients and the variables of the terms involved. For example, in the terms 6x and -4y, the GCF is 2, as it is the largest number that divides both coefficients.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and can make solving equations easier. In the given expression, recognizing that both terms share a common factor allows us to factor it out, leading to a simpler form, which is essential for further manipulation or solving.

Distributive Property

The Distributive Property states that a(b + c) = ab + ac, allowing us to distribute a factor across terms within parentheses. This property is crucial when factoring, as it helps to reverse the process of distribution. In the example, recognizing that both terms share the factor (a + b) enables us to factor it out, demonstrating the application of this property.