Factoring Binomial Using Distributive Property
Factoring a binomial using the distributive property involves expressing the
binomial as a product of common factors. Here’s a step-by-step explanation:
1. Identify the Greatest Common Factor (GCF): Find the greatest common
factor of the terms in the binomial. The GCF is the largest factor that divides
both terms.
2. Rewrite the Binomial: Express each term of the binomial as a product of the
GCF and another factor.
3. Apply the Distributive Property: Factor out the GCF from the binomial,
using the distributive property in reverse.
Example:
Consider the binomial 6x+9:
1. Identify the GCF
The GCF of 6 and 9 is 3.
2. Rewrite the Binomial
6x + 9 = 3⋅2x + 3⋅3
3. Apply the Distributive Property
6x + 9 = 3(2x+3)
So, 6x+9 factored using the distributive property is 3(2x+3).
Example 2
Binomial: 8y+12
1. Identify the GCF: The GCF of 8 and 12 is 4.
2. Rewrite the Binomial: 8y+12=4⋅2y+4⋅3
3. Apply the Distributive Property: 8y+12=4(2y+3)
So, 8y+12 factored using the distributive property is 4(2y+3)
