Combine Like Terms I can simplify expressions with several variables by combining like terms.

Constant Vocabulary A number with nothing else attached to it. Examples: 1, 2, 47, 925

Variable Vocabulary A letter that represents an unknown number. Examples: a, b, x, y

Coefficient Vocabulary The number in front of the variable. Examples: 3x 3 is the coefficient 2x 2 is the coefficient

Like Terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents). Examples: 4x and -3x or 2y2 and –y2

Like terms because each term consists of a single variable, x, and a numeric coefficient: 2x, 45x, x, 0x, -26x, -x Like terms because they are all constants: 15, -2, 27, 9043, 0.6 Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²

What are unlike terms? The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5 Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy

Combine Like Terms I can simplify expressions with several variables by combining like terms.

Like Terms – same variable with same exponent Key Skills Like Terms – same variable with same exponent Simplify When combining like terms, only use the coefficients. 6x + 2x = 6x + 2x = 8x Simplify 4x + 3y – 2x + 4y = 2x + 7y Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.

5 cats + 3 cats 8 cats

5a + 3a 8a

5 apples + 3 oranges 5 apples + 3 oranges

5 cats + 3 dogs 5 cats + 3 dogs

You Try 3y + 2 + 3x – y + 5x x + x

The Distributive Property Expressions with variables: Simplify 5(3n + 4). No symbol between the 5 and the parenthesis indicates a multiplication problem. Distribute by multiplication: 15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.

The Distributive Property Simplify 4(7n + 2) + 6. No symbol between the 4 and the parenthesis indicates a multiplication problem. The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.

Distributive Property Step 1) Use the Distributive Property 3 (2x – 5) - 2x Step 2) Combine Like Terms 6x – 15 – 2x *** 6x and 2x are like terms!!!! Step 3) Simplified Expression 4x – 15

Distributive Property Example: 6(a + 3) Use the Distributive Property (6a) + (6 x 3) Multiply 6a + 18 Simplified ***CAN NOT add 6a + 18 together because they are not like terms.

Practice Problems Solve: 2x + 6(x + 1) Explain how each of the below answers are wrong and why. 2x + 6x + 1 9x