Vocabulary
In an expression, the parts being added together or subtracted. Example: 4x + 3x + 3y + 7y
Term
8a + 15a + a + 9
24a + 9
21b - 11b - 10 - 2b
8b - 10
3(7x2)
21x2
7x + 7
NOT Like Terms
7x + 7
Terms that contain the same variable(s) raised to the same exponent. These terms can be combined. Example: 3x + 9x or 7y + 3y
Like Terms
5x + 35 + 3x + 2
8x + 37
12c - 6c - 30
6c + 30
2(x2 + y)
2x2 + 2y
3x + 15x
Like Terms
18x
A mathematical phrase that contains numbers, operations, and/or variables (but no = sign). Example: 5x + 4y + 5 - 2x
Expression
32 + 12t + 16t + 8
28t + 40
5z + 55 - 26 - z
4z - 29
3(2m3 + 2n)
6m3 + 6n
3m5n3 + 9m5n3
Like Terms
12m5n3
- To perform all indicated operations, including combining like terms.
- When you do this you do not always get a number answer like 25 or 10.
- Frequently you get an expression as an answer, like 2x + 5
What is Simplify?
3x2y + 4xy + 4xy + 6
3x2y + 8xy + 6
3 + 13x + 3x2 - 5x - 2x2
x2 + 9x + 3
4(2x + 3xy)
8x + 12xy
15x3yz - 5x3yz
Like Terms
15x3yz - 5x3yz
A symbol, usually a letter of the alphabet, used to represent an unknown value.
Variable
7m + 6m4n3 + 3m + 4m4n3
10m + 10m4n3
8p + 3p3 + 13 - 4p2 - 2 - 6p
3p3 - 4p2 + 2p + 11
4x(2 + 3)
20x
22r5s3t - 3r5s3t2
NOT Like Terms
22r5s3t - 3r5s3t2
a mathematical expression composed of variables, coefficients, and exponents where the only operations used are addition, subtraction, and multiplication,
polynomial
2(x4 + 3x4)
8x4
2(6x4 - 3x4)0
20(x4 + 3x4)
4x4
What is most important to focus on when combining like terms?
variables and exponents match!