Warm Up
Write an algebraic expression:
1) Seven less than x
2) The product of 7 and y
3) The quotient of 15 and x
4) Ten taken from the product of
six and n.
5) Name the three main
properties of numbers and give
an example of each.
Combining Like Terms
Prior Knowledge required and resources:
Integer review => www.ixl.co…7th grade..E.1 through E.9;
Big Ideas textbook (red) Chapter 1 lessons 1 through 3.
Laws of Exponents => www.ixl.com.. 8th grade..F.8 through
F.12 ; Big Ideas textbook (blue) chapter 9 lessons 2 through
4
Distributive Property => www.ixl.com..6th grade P.18; Big
Ideas textbook (blue) Chapter 1 lesson 2
Key Vocabulary
Constant
Variable
Coefficient
Exponent
Vocabulary
Constant
A number with nothing else attached to it.
Examples: 1, 2, 47, 925, -4
Vocabulary
Variable
A letter that represents an unknown number.
Examples: a, b, x, y
Vocabulary
Coefficient
The number in front of the variable.
Examples: 3x
-2x
Remember:
3x = 3 times x
3 is the coefficient
-2 is the coefficient
Vocabulary
Exponent
The number “on top” of the variable.
Example: x³
3 is the exponent
General Overview
TERMS can be;
Numbers => Constants => 2, -4, 67, 0.53, 3/4
Variables => a, x, y
Product of a Number and Variable => 3x, -57z, 89.4t
Product of Variables => mn, xy, ac
Variable raised to a power => v3, x2
LIKE TERMS are;
All numbers => 2 & 56 are like terms => 8 & 6/8 are like terms.
Terms with the same variable and the same exponent. => m2 & m2 are like terms => 3z
& 5z are like terms. => x2y4 & 10x2y4 are like terms.
COMBINE;
You can add or subtract terms that are alike.
2 – 56 = -54
8 + 6/8 = 8.75
m2 + m2 = 2m2
3z – 5z = -2z
x2y4 + 10x2y4 = 11x2y4
Terms Are separated by a
sign
(- or +)
How many terms are in the
example?
Coefficient it is the number next
to the variable. You must have a
variable to have a coefficient.
Any variable without a number
in front of it has an understood
coefficient of 1.
Constant a number without a
variable
Combine Like Terms
(put the same variables together!)
Practice on your own
That is the answer…don’t do anything else!
6y + 2x + 4y + 8
6y + 2x + 4y + 8
2x + 10y + 8
7n + 6y + 3 – 2n + 4
7n + 6y + 3 – 2n + 4
5n + 6y + 7
3r + 7y -2r + y
3r + 7y -2r + y
r + 8y
4n + 9 + 6m - n - 2m + 2
4n + 9 + 6m - n - 2m + 2
4m + 3n + 11
2x + 7 + 5x - 4 - x
2x + 7 + 5x - 4 - x
6x + 3
5 + 7x + 2x – 3 + 6
5 + 7x + 2x – 3 + 6
9x + 8
x + y + 4x – 3x + 2y + 3y
x + y + 4x – 3x + 2y + 3y
2x +6y
3x² + 5x +17 + 6x + 20
3x² + 5x +17 + 6x + 20
11x+ 3x² +37
4x + x² +12 – 4 +2x
4x + x² +12 – 4 +2x
x² +6x + 8
12y + 12x +12 – 6x + 12
12y + 12x +12 – 6x + 12
12y + 6x + 24
12y + 4 +x –7y + 8 +8x
12y + 4 +x –7y + 8 +8x
5y + 9x +12
5x + x²+ 2x + 5 – 4 - x²
5x + x²+ 2x + 5 – 4 - x²
7x + 1
5x² + 8x + 7x²+6x
5x² + 8x + 7x²+6x
12x² +14x
12x + 6 –8x –4x –3 + 12
12x + 6 –8x –4x –3 + 12
15
5x + 4 –3x +5 +2x - 9
5x + 4 –3x +5 +2x - 9
4x
4x +2y + 8 – 3 - y - x
4x +2y + 8 – 3 - y - x
3x + y + 5
4(2m + 3) – 5
4(2m + 3) – 5
8m + 12 – 5
8m + 7
3(4c + 2n) + 4 – 2c
3(4c + 2n) + 4 – 2c
12c + 6n + 4 – 2c
10c + 6n + 4
5(x + 2) + x + 7
5(x + 2) + x + 7
5x + 10 + x + 7
6x + 17
x(4 + 7) + 4x + y
x(4 + 7) + 4x + y
4x + 7x + 4x + y
15x + y
x + 2(3x + 4y) + 3
x + 2(3x + 4y) + 3
x + 6x + 8y + 3
7x + 8y + 3
4x + 5 +7x + 2y +2 - y
4x + 5 +7x + 2y +2 - y
11x + y + 7
2y + 2x + 8 – 6 + x – 2y
2y + 2x + 8 – 6 + x – 2y
3x + 2
4x + 6y + 6 + 7x + y
4x + 6y + 6 + 7x + y
11x + 7y + 6
3x² + 4x –2x² -3x +2x
3x² + 4x –2x² -3x +2x
x² + 3x
8x + 4 – 4 – 4x +x
8x + 4 – 4 – 4x +x
5x
y + 5x + 6y + 9 - 6
y + 5x + 6y + 9 - 6
5x + 7y + 3
x² +3 +2x² + 4 -7
x² +3 +2x² + 4 -7
3x²
5y + 3 + 7x² -2x - x² + y
5y + 3 + 7x² -2x - x² + y
6x² + 6y -2x+3