1) Translate 2) ????? 3) Solve 3) Check

What animals are on the next slide?

We say the above is, 2 Dogs and 2 Sharks and 3 frogs and 4 Lions and 1 Bird 2d + 2S + 3f + 4L + 1B We combine things that are alike!

y v r y j v y j r r j j r v v r

yyy rrrrr vvvv jjjj 3y 5r 4v 4j

So, how about this? X + R + Y + X + X + X + Y + R + Z What would this be…simplified! 4X + 2R + 2Y + Z WE DON’T SAY, 1z! IF THERE IS ONLY ONE “z”, THEN WE WRITE “z”

So, how about this? B + Q + B + Q +B + G + B + B + G What would this be…simplified! 5B + 2Q + 2G

Terms in an expression are separated by plus or minus signs. Like terms can be grouped together because they have the same variable raised to the same power. Equivalent expressions have the same value for all values of the variables.

So, how about this? 3X + 2Y + K + 4X + 3Y What would this be…simplified! 7X + 5Y + K

So, how about this? 6m + 4z + Q + 3m + 3z What would this be…simplified! 9m + 7z + Q

So, how about this? 14m + 4z + Q - 10m - 3z -z What would this be…simplified! 4m + Q 24m + 8z + Q WRONG!

So, how about this? 6m - 4z + Q - 3m + 3z What would this be…simplified! 3m - z + Q

So, how about this? 5r – 4k - p - r + 7k - 2p – k + f What would this be…simplified! 4r +2k -3p + f

So, can you simplify What would this be…simplified! 8

So, can you simplify 5(2) What would this be…simplified! 11

To simplify an expression, perform all possible operations, including combining like terms.

Combine like terms. Additional Example 1: Combining Like Terms To Simplify Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y. Combine coefficients: 7 – = 5 and 8 – 1 = 7 5y + 7

Combine like terms. Try This: Example 1 Identify like terms; the coefficient of q is 1, because 1q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6 3q3q A. 4q – q B. 5c + 8 – 4c – 2 – c

Combine like terms. Additional Example 2A: Combining Like Terms in Two-Variables Expressions Identify like terms. Combine coefficients: 9 – 2 = 7 A. 9x + 3y – 2x + 5 7x + 3y + 5 9x + 3y – 2x + 5

Combine like terms. Additional Example 2B: Combining Like Terms in Two-Variable Expressions Identify like terms. Combine coefficients: 5 – 2 = 3 and 7 – 3= 4 B. 5t + 7p – 3p – 2t 3t + 4p 5t + 7p – 3p – 2t

Combine like terms. Additional Example 2C: Combining Like Terms in Two-Variable Expressions No like terms. C. 4m + 9n – 2 4m + 9n – 2

Combine like terms. Try This: Example 2 Identify like terms. Combine coefficients: = 7 A. 2x + 5x – 4y + 3 7x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 B. 9d + 7c – 4d – 2c 5d + 5c 9d + 7c – 4d – 2c No like terms. C. 8g + c – 6 8g + c – 6

Lesson Quiz Combine like terms. 1. 3x x 2. 13k + 6  8k k Simplify. 3. 4(3x + 6)  7x 4. 6(x + 5) + 3x Solve. 5. 6y + y = The accounting department ordered 15 boxes of pens. The marketing department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens? 6k + 15 y = 6 5x + 4 5x + 249x + 30 $3

To simplify an expression, perform all possible operations, including combining like terms.

Simplify 6(5 + n) – 2n. Additional Example 3: Simplifying Algebraic Expressions by Combining Like Terms Distributive Property. 6n and 2n are like terms. 6(5 + n) – 2n n – 2n 6(5) + 6(n) – 2n n Combine coefficients 6 – 2 = 4

Simplify 3(c + 7) – c. Try This: Example 3 Distributive Property. 3c and c are like terms. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients 3 – 1 = 2

Solve x + 3x = 48. Additional Example 4: Solving Algebraic Expressions by Combining Like Terms Identify like terms. The coefficient of x is 1. Combine coefficients: = 4 x + 3x = 48 4x = 48 x = 12 Divide both sides by

Solve 7c – c = 102. Try This: Example 4 Identify like terms. The coefficient of c is 1. Combine coefficients: 7 – 1 = 6 7c – c = 102 6c = 102 c = 17 Divide both sides by

Terms in an expression are separated by plus or minus signs. Like terms can be grouped together because they have the same variable raised to the same power. Equivalent expressions have the same value for all values of the variables.