term coefficient constants 7y, -2, 13 7 -2, 13 y, 9x, 9, x
TRANSCRIPT
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COMBINING LIKE TERMS
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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=9Term Term Term
Coefficient
Constants
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EXAMPLE
7Y-2+9X=13TERMS:
COEFFICIENTS:
CONSTANTS:
VARIABLES:
7y, -2
, 13
7
-2, 13Y
, 9x
, 9
, X
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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
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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
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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
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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)
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Combine like terms
By combining apples with apples and oranges with oranges, you get...
+
1 apple
3 apples + 2 oranges +(- 2) apples + 2 oranges
+ 4 orangescoefficients
+ – +
+ +( – ) +
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EXAMPLE
=4 +2 +(-2 )+(-1 ) = + +
+
4 + 2 -2-1
= + =2 +1
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CHANGE EVERYTHING TO ADDITION
2X + (-3Y) + 5X + 3Y + 12REORDER YOUR TERMS
2X+5X+(-3Y)+(3Y)+12FIND THE LIKE TERMS
2X +5X +(-3Y) +3Y +12COMBINE LIKE TERMS
7X +12
Example: Simplify 2x - 3y + 5x + 3y + 12
Remember: adding the
opposite cancels out so
(-3x)+(3x)=0
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SIMPLIFY:
Reorder the terms
Combine like terms (simplify)
4x2-13y+4x+12x2-3x+3
4x2 +12x2+ 4x +(-3x)+(-13y)+3
16x2 + x + (-13y) + 3
Change all operations to addition using keep-change-change
4x2 +(-13y) +4x +12x2 +(-3x) +3
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Combine like terms
Identify like terms.
Combine coefficients: 14 – 5 = 9
A. 14a – 5a
9a
Change any subtraction to addition
14a +(-5a)Reorder Terms
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B. 7y + 8 – 3y – 1 + y
Combine like terms
Change any subtraction to addition
7y +(-3y)+y
Identify like terms ; the coefficient of y is 1, because 1y = y.+8 +(-1)
Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7
Reorder Terms
5y + 7
7y +8 +(-3y) +(-1) +y
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3q
C. 4q – q
Identify like terms ; the coefficient of q is 1, because 1q = q.
Combine coefficients: 4 +(-1) = 3.
4q +(-1q)
Combine like terms (on the boards).
Change any subtraction to addition
Reorder Terms
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D. 5c + 8 – 5c – 2
6
Combine like terms (on the boards).
5c +(-5c) +8 +(–2)
Combine coefficients: 4 +(-1) = 3.
Change any subtraction to addition
Identify like terms ; the coefficient of q is.
Reorder Terms
5c + 8 +(-5c) +(–2)
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F. 5m2 – 7m – 8 + 4
5m2 – 7m – 4
Combine like terms (on the boards).
Combine coefficients: 4 +(-1) = 3.
Change any subtraction to addition
Identify like terms ; the coefficient of q is.
Reorder Terms
5m2 +(-7m) + (-8) + 4
5m2 +(-7m) +(-8) +4
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E. 4m + 9n – 2
4m + 9n – 2
No like terms.
Combine like terms (in your notes).
Combine coefficients.
Change any subtraction to addition
Identify like terms ; the coefficient of q is.
Reorder Terms
4m +9n +(-2)