Objectives Combining like terms.

The terms of an expression are the parts to be added or subtracted The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4x – 3x + 2

A coefficient is a number multiplied by a variable A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. Coefficients 1x2 + 3x

Example 3A: Combining Like Terms Simplify the expression by combining like terms. 7p – 5p 18y2 + 2y2 13w3 – 4w 7p – 5p 18y2 + 2y2 13w3 – 4w 2p 20y2 13w3 – 4w

Example 3A: Combining Like Terms Simplify the expression by combining like terms. 12m + 4n 8r3 + 3r3 10a – 7a 12m + 4n 8r3 + 3r3 10a – 7a 12m + 4n 11r3 3a

Example 3C: Combining Like Terms Simplify the expression by combining like terms. 5m + 2 – 3m 20t2 + 6t + 4t – 15t2 5m + 2 – 3m 20t2 + 6t + 4t – 15t2 2m + 2 5t2 + 6t + 4t 5t2 + 10t

Example 4: Simplifying Algebraic Expressions Simplify 7x + 4(3 + 2x). Justify each step. Procedure Justification 1. 7x + 4(3 + 2x) 2. 7x + 4(3) + 4(2x) Distributive Property 3. 7x + 12 + 8x Multiply. Commutative Property 4. 7x + 8x + 12 5. (7x + 8x) + 12 Associative Property 6. 15x + 12 Combine like terms.

Check It Out! Example 4a Simplify -6(x – 4) + 9. Justify each step. Procedure Justification 1. -6(x – 4) + 9 2. -6(x) – 6(-4) + 9 Distributive Property 3. -6x + 24 + 9 Multiply. Combine like terms. 4. -6x + 33

Check It Out! Example 4b Simplify −12x – 5x + 3a + x. Justify each step. Procedure Justification 1. –12x – 5x + 3a + x 2. –17x + x + 3a Commutative Property 3. –16x + 3a Combine like terms.

Lesson Quiz: Part II Simplify each expression by combining like terms. Justify each step with an operation or property. 5. 6. 14c2 – 9c 14c2 – 9c 7. -2(3x – 4) + 2x (-6x + 8) + 2x = -4x + 8 8. 24a + b2 + 3a + 2b2 27a + 3b2