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

Another example… • 10 x – 4 y + 3 x 2 + 2 x – 2 y 3 x 2 Remember you cannot 10 x, 2 x combine terms with the same variable but different exponents. -4 y – 2 y • 3 x 2 + 12 x – 6 y

Now you try… Simplify the following: • 5 x + 3 y - 6 x + 4 y + 3 z • 3 b - 3 a - 5 c + 4 b • 4 ab – 2 a 2 b + 5 – ab + ab 2 + 2 a 2 b + 4 • 5 xy – 2 yx + 7 y + 3 x – 4 xy + 2 x A A

You Try #1 • Simplify the following: 1. 5 x + 3 y - 6 x + 4 y + 3 z 5 x, -6 x 3 y, 4 y 3 z -x + 7 y + 3 z

You Try #2 • Simplify the following: 2. 3 b - 3 a - 5 c + 4 b 3 b, 4 b -3 a -5 c -3 a + 7 b – 5 c

You Try #3 • Simplify the following: 3. 4 ab – 2 a 2 b + 5 – ab + ab 2 + 2 a 2 b + 4 4 ab, -ab -2 a 2 b, 2 a 2 b 5, 4 ab 2 3 ab + ab 2 + 9

You Try #4 • Simplify the following: 4. 5 xy – 2 yx + 7 y + 3 x – 4 xy + 2 x 5 xy, -2 yx, -4 xy 7 y 3 x, 2 x -xy + 7 y + 5 x