Objectives Simplify expressions with several variables by combining like terms.

Glossary Terms Coefficient Variable Exponent Term Like Terms Simplified

Some Things to Remember Just Watch What Happens x 1x +1x1 1 +1x +1x1

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.

+ 7x 7x + 3y + 3y + 5y + 5y – 9x – 9x – 17y – 17y = – 2x – 2x = – 9y Just Watch What Happens + 7x 7x + 3y + 3y + 5y + 5y – 9x – 9x – 17y – 17y = – 2x – 2x = – 9y – 9y

3 + 5x = 3 + 5x ≠ 8x 3(5x) = 15x TRY THESE 1) 3q + 7q = 10q Your welcome 2) 4x + 8y – 10x + 3y = 4x + 8y – 10x + 3y = – 6x + 11y Review Again 3 + 5x = 3 + 5x ≠ 8x 3(5x) = 15x

In algebraic terms, find the perimeter of the following shape. 4x + 3y Key Skills 3x – 2y 3x – 2y 2x To find the perimeter, add the sides together. P = 3x – 2y + 2x + 3x – 2y + 4x + 3y = 12x – y What is the perimeter if x = 5 and y = 8? P = 12(5) – 8 = 52

Find the perimeter of the following shape when x = 2. TRY THIS 5x + y 5x + y 6x – 2y To find the perimeter, add the sides together. P = 5x + y + 5x + y + 6x – 2y = 16x = 32 Does the value of y matter in this problem? Obviously Not!

A farmer has two rectangular fields. TRY THIS He wants to put a fence around both. In algebraic terms, how much fence would he need? 3x – 6 2x + 5 Field 2 4 Field 1 3 P1 = 3 + 3 + 2x + 5 + 2x + 5 P2 = 4 + 4 + 3x – 6 + 3x – 6 P1 = 4x + 16 P2 = 6x – 4 How much fence would the farmer need if x = 5? Ptotal = 4x + 16 + 6x – 4 Ptotal = 10x + 12 Ptotal = 10(5) + 12 Ptotal = 62

“Your Turn” 7t – 4t = 24 6y – 8y – y = 27 -3s + 8s – 10s = 35 18a – 14a = 36 -5x + 7x – 10x = 48 10z + 2z – 13z = 45 -12r + 15r = 21 -3b – 5b – 2b = 80