Simplify the following Expression: 2 3 𝑥 − 1 4 ( 4 5 𝑥 – 8) + 1 2

Objective In this lesson you will learn how to factor linear expressions with rational coefficients by using the distributive property.

Greatest Common Factor: What is the GCF of 24 and 32? Let’s Review Even though 24 and 32 have 1, 2, 4, and 8 in common, the greatest of these is 8.

A Common Mistake A common mistake students make is to use a common factor that is not the greatest common factor.

Remember - Distributive Property: Simply multiply the term outside of the parentheses by the term(s) inside the parentheses. EX: 3(2x -4) = 6x – 12 Let’s Review Even though 24 and 32 have 1, 2, 4, and 8 in common, the greatest of these is 8.

4x + 8 Example 1 Factor the expression: Core Lesson To factor by using the distributive property, we must first identify the greatest common factor of the coefficient and the constant term. In this case, the coefficient is 4 and the constant term is 8. Examine factors of 4 and 8, conclude that 4 is the GCF. Then express each term as the product of 4 and another factor. Now we can write 4x + 8 as 4(x) + 4(2). By the distributive property, this is equal to 4(x + 2). Coach’s Commentary The most common errors in factoring are: 1) using a common factor less than the GCF, and 2) subtracting the common factor rather than dividing it. Remind the students that factoring is a division process, not a subtraction process.

Once you have found the GCF: Pull the GCF to the front of the parentheses. Divide each term by the GCF. Leave the quotient inside of the parentheses. Core Lesson To factor by using the distributive property, we must first identify the greatest common factor of the coefficient and the constant term. In this case, the coefficient is 4 and the constant term is 8. Examine factors of 4 and 8, conclude that 4 is the GCF. Then express each term as the product of 4 and another factor. Now we can write 4x + 8 as 4(x) + 4(2). By the distributive property, this is equal to 4(x + 2). Coach’s Commentary The most common errors in factoring are: 1) using a common factor less than the GCF, and 2) subtracting the common factor rather than dividing it. Remind the students that factoring is a division process, not a subtraction process.

24x - 32 Example 2 Factor the expression: Core Lesson To factor by using the distributive property, we must first identify the greatest common factor of the coefficient and the constant term. In this case, the coefficient is 4 and the constant term is 8. Examine factors of 4 and 8, conclude that 4 is the GCF. Then express each term as the product of 4 and another factor. Now we can write 4x + 8 as 4(x) + 4(2). By the distributive property, this is equal to 4(x + 2). Coach’s Commentary The most common errors in factoring are: 1) using a common factor less than the GCF, and 2) subtracting the common factor rather than dividing it. Remind the students that factoring is a division process, not a subtraction process.

24x - 32 Example 2 Factor the expression: Core Lesson To factor by using the distributive property, we must first identify the greatest common factor of the coefficient and the constant term. In this case, the coefficient is 4 and the constant term is 8. Examine factors of 4 and 8, conclude that 4 is the GCF. Then express each term as the product of 4 and another factor. Now we can write 4x + 8 as 4(x) + 4(2). By the distributive property, this is equal to 4(x + 2). Coach’s Commentary The most common errors in factoring are: 1) using a common factor less than the GCF, and 2) subtracting the common factor rather than dividing it. Remind the students that factoring is a division process, not a subtraction process.

Guided Practice Factor: 12x - 18 Answer: 6(2x - 3)

Extension Activities For a student who gets it and is ready to be challenged further: Factor: – 3x – 18 Answer: – 3(x + 6)

Extension Activities For a student who gets it and is ready to be challenged further: Factor 2m + 19 + 6m - 7 Answer: 4(2m + 3)

Let’s Review Even though 24 and 32 have 1, 2, 4, and 8 in common, the greatest of these is 8.