write each binomial as an equivalent product of its greatest common factor and some other binomial.

To write each binomial as an equivalent product of its greatest common factor (GCF) and some other binomial, you need to:

1. Identify the greatest common factor of the terms in the binomial.
2. Factor out the GCF from the binomial.

Let's go through an example:

**Example 1:**

Binomial: \( 6x + 12 \)

Step 1: Find the GCF of \( 6x \) and \( 12 \).
- The GCF of 6 and 12 is 6.
- Since there is no common variable in both terms, the GCF is just 6.

Step 2: Factor out the GCF:
- \( 6x + 12 = 6(x + 2) \).

So, the binomial \( 6x + 12 \) can be written as the product of its GCF and another binomial: \( 6(x + 2) \).

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**Example 2:**

Binomial: \( 15y^2 - 10y \)

Step 1: Find the GCF of \( 15y^2 \) and \( 10y \).
- The GCF of 15 and 10 is 5.
- The GCF of \( y^2 \) and \( y \) is \( y \).

So, the GCF is \( 5y \).

Step 2: Factor out the GCF:
- \( 15y^2 - 10y = 5y(3y - 2) \).

Thus, \( 15y^2 - 10y \) can be factored as \( 5y(3y - 2) \).

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If you have any specific binomials you'd like help factoring, feel free to share them!

Would you like more details or clarifications on any step?

Here are 5 related questions to explore this topic further:

1. How do you find the greatest common factor (GCF) of two terms in a binomial?
2. Can a binomial always be factored by its GCF?
3. How does factoring help solve equations involving binomials?
4. What happens if the terms of a binomial have no common factors?
5. Can the GCF of a binomial include variables as well as constants?

**Tip:** When factoring, always double-check by distributing the GCF back to ensure it gives the original binomial!

Write each binomial as an equivalent product of its greatest common factor and some other binomial.

Learn how to factor binomials by finding the greatest common factor (GCF). This lesson covers examples like 6x + 12 and 15y^2 - 10y, offering a clear step-by-step guide for students in Grades 6-8.

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