Combine Like Terms I can simplify expressions with

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

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

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

Vocabulary Coefficient The number in front of the variable. Examples: 3 x 2 x 3 is the coefficient 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: 4 x and -3 x or 2 y 2 and – y 2

• Like terms because each term consists of a single variable, x, and a numeric coefficient: 2 x, 45 x, x, 0 x, -26 x, -x • Like terms because they are all constants: 15, -2, 27, 9043, 0. 6 • Like terms because they are all y² with a coefficient: 3 y², -y², 26 y²

What are unlike terms? • The following two terms both have a single variable, but the terms are not alike since different variables are used: 17 x, 17 z • Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15 y, 19 y², 31 y 5 • Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19 x, 14 xy

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

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

5 cats + 3 cats 8 cats

5 a + 3 a 8 a

5 apples + 3 oranges

5 cats + 3 dogs

You Try • 3 y + 2 + 3 x – y + 5 x • x+x

The Distributive Property • Expressions with variables: Simplify 5(3 n + 4). • No symbol between the 5 and the parenthesis indicates a multiplication problem. Distribute by multiplication: 15 n and 20 are not alike and therefore cannot be combined. The answer 15 n + 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(7 n + 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 28 n + 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 (2 x – 5) - 2 x Step 2) Combine Like Terms 6 x – 15 – 2 x *** 6 x and 2 x are like terms!!!! Step 3) Simplified Expression 4 x – 15

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

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