Combining Like Terms

3x-4=9 What is a term? A part of an equation or expression Coefficient- A number used to multiply a variable Constant- A number on its own 3x-4=9 Coefficient Constants Term Term Term

7y-2+9x=13 Example Terms: Coefficients: Constants: Variables: 7y , -2 , 13 , 9x 7 , 9 -2 , 13 Y , X

What EXACTLY does the same or “Like” mean? Terms with the same variable or variables and raised to the same power Same: 5x and 12x Same: 10 and 7 Same: 9z and 14z Same: 8y 5x, 8y, 9z, 10, 12x, 14z, 7

Document camera I couldn’t find a very fun video but I did really like the way the woman explained the concept in these videos so I think I’ll just use the document camera to do a shorter version of what she did in these following videos http://www.virtualnerd.com/algebra-1/algebra-foundations/simplifying- expressions/simplifying-expressions-examples/like-terms-definition http://www.virtualnerd.com/algebra-1/algebra-foundations/simplifying- expressions/simplifying-expressions-examples/add-like-terms-example

What is Combining like terms If numbers have a variable, then you can combine only ones that have the same variable Also if numbers don’t have variables they can only be combined with other numbers that don’t have variables Like terms could be combined by adding their coefficients

How To Combine like Terms First, change our operators to addition by using keep- change-change Second, Reorder the expression so like terms are next to each other Finally, combine like terms by adding their coefficients (simplify)

+ – + + +( – ) + + Combine like terms + – + + +( – ) + By combining apples with apples and oranges with oranges, you get... + Emphasize equivalent equations 3 apples + 2 oranges +(- 2) apples + 2 oranges coefficients 1 apple + 4 oranges

4 + 2 -2 -1 =4 +2 +(-2 )+(-1 ) = + + + = + =2 +1 Example Good Movies 4 + 2 -2 -1 =4 +2 +(-2 )+(-1 ) = + + + No notes = + =2 +1

Remember: adding the opposite cancels out so Example: Simplify 2x - 3y + 5x + 3y + 12 Change everything to addition 2x + (-3y) + 5x + 3y + 12 Reorder your terms 2x+5x+(-3y)+(3y)+12 Find the like terms 2x +5x +(-3y) +3y +12 Combine like terms 7x +12 Remember: adding the opposite cancels out so (-3x)+(3x)=0

Simplify: 4x2-13y+4x+12x2-3x+3 4x2 +(-13y) +4x +12x2 +(-3x) +3 Change all operations to addition using keep-change-change 4x2 +(-13y) +4x +12x2 +(-3x) +3 Reorder the terms Before bringing up the first step ask the students where we will need to apply kcc This slide will allow me to emphasize how like terms also must include variable to the same power Have the students do this problem on their whiteboards 4x2 +12x2+ 4x +(-3x)+(-13y)+3 Combine like terms (simplify) 16x2 + x + (-13y) + 3

Combine like terms A. 14a – 5a 14a +(-5a) 9a Change any subtraction to addition 14a +(-5a) Reorder Terms For the first example I can also pose the question: what if I had 14a and just -5, would I have like terms? If I get asked why we have to apply keep change change to the first example I’ll let students know that examples are going to get more complicated so we want you to get in the habit of applying this process while the problems are easier First problem in their notes, second problem on the white boards Identify like terms. 9a Combine coefficients: 14 – 5 = 9

Combine like terms B. 7y + 8 – 3y – 1 + y 7y +8 +(-3y) +(-1) +y Change any subtraction to addition B. 7y + 8 – 3y – 1 + y Reorder Terms 7y +8 +(-3y) +(-1) +y Identify like terms ; the coefficient of y is 1, because 1y = y. 7y +(-3y)+y +8 +(-1) Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7 5y + 7

Combine like terms (on the boards). Change any subtraction to addition C. 4q – q Reorder Terms 4q +(-1q) Identify like terms ; the coefficient of q is 1, because 1q = q. 3q Combine coefficients: 4 +(-1) = 3.

Combine like terms (on the boards). D. 5c + 8 – 5c – 2 Change any subtraction to addition 5c + 8 +(-5c) +(–2) Reorder Terms 5c +(-5c) +8 +(–2) Identify like terms ; the coefficient of q is. 6 Combine coefficients: 4 +(-1) = 3.

Combine like terms (on the boards). F. 5m2 – 7m – 8 + 4 Change any subtraction to addition 5m2 +(-7m) + (-8) + 4 Reorder Terms 5m2 +(-7m) +(-8) +4 Identify like terms ; the coefficient of q is. Combine coefficients: 4 +(-1) = 3. 5m2 – 7m – 4

Combine like terms (in your notes). E. 4m + 9n – 2 4m +9n +(-2) Change any subtraction to addition Reorder Terms 4m + 9n – 2 Identify like terms ; the coefficient of q is. Combine coefficients. No like terms.