Bell Work Simplify the expression: 1. 2(x +4) 2. 4x + 3y – x + 2y 3. 3(x – 6) x Answers: 2x+ 8 3x + 5y 11x – 14

Combining Like Terms and Distributive Property

Combining Like Terms and the Distributive Property In this lesson, you will review how to combine like terms and how to use the distributive property. You will then use them together.

Terms in an algebraic expression are separated by addition or subtraction signs. How many terms are in this expression? Like terms are terms that look alike. So, what are like terms?

More specifically, Like Terms are terms that have the same variable raised to the same power (exponent). Now, let’s give this a try.

Collecting Like Terms Example Reorder the terms. Combine like terms.

Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y. 5y + 7 Combine coefficients: 7 – = 5 and 8 – 1 = 7

Combine like terms. Identify like terms; the coefficient of q is 1, because 1q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. 6 3q3q C. 4q – q D. 5c + 8 – 4c – 2 – c Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6

E. 4m + 9n – 2 4m + 9n – 2 Combine like terms. No like terms. F. 5m – 7m – m – 4

Remember, to simplify an expression means to perform all possible operations, including combining like terms. In other words, simplify means solve!

The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. For any numbers a, b, and c, a(b + c) =a(b) + a(c) and a(b – c) =a(b) – a(c)

Distribute A. 6(x - 3) B. -2(y + 1) C. -3(a - 1) 6x y + (-2) -3a – (-3)

Now we will use the distributive property first, then combine like terms second.

1. Simplify 6(5 + n) – 2n. Distributive Property. Multiply. 6(5 + n) – 2n n – 2n 6(5) + 6(n) – 2n n Combine coefficients 6 – 2 = 4.

2. Simplify 3(c + 7) – c. Distributive Property. Multiply. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients 3 – 1 = 2.

3. 4(3x + 6)  7x 4. 6(x + 5) + 3x Simplify. Distributive Property. Multiply. Combine coefficients = 5. 4(3x) + 4(6) – 7x 12x + 24 – 7x 5x + 24 Distributive Property. Multiply. Combine coefficients = 9. 6(x) + 6(5) + 3x 6x x 9x + 30

5. 5(2x - 3) + 4x 10x – x 14x - 15 Simplify.

Practice: Worksheet!!