combining like terms - monroe.k12.nj.us€¦ · like terms –part i they have the same variables...
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Combining Like Terms
SIMPLIFYING EXPRESSIONS
WITH SEVERAL VARIABLES
LIKE TERMS – PART I They have the same variables or the same exponents
Can be combined
When combining like terms, only combine the coefficients
Example: Simplify the expression below
𝟔𝒙 + 𝟐𝒙𝟖𝒙
LIKE TERMS – PART IIExample: Simplify the expression below.
𝟒𝑥 + 𝟑𝑦 − 𝟐𝑥 + 𝟒𝑦
𝟐𝑥 + 𝟕𝑦
LIKE TERMS – PART III NEVER combine variables with different variable terms.
Example: 2𝑥 + 7𝑦 ≠ 9𝑥𝑦
NEVER combine constant terms with variable terms.
Example: 3𝑎 + 6 ≠ 9𝑎
LIKE TERMS – PROBLEM #1
Simplify the following expression below. Combine like terms if possible.
𝟕𝒂 + 𝟑𝒂
10a
LIKE TERMS – PROBLEM #2
Simplify the following expression below. Combine like terms if possible.
𝟏𝟎𝒃 − 𝟒𝒃
6b
LIKE TERMS – PROBLEM #3
Simplify the following expression below. Combine like terms if possible.
𝟏𝟏𝒃 + 𝟔𝒏
11b + 6n
LIKE TERMS – PROBLEM #4
Simplify the following expression below. Combine like terms if possible.
𝟏𝟐𝒏 + 𝟕𝒏
19n
LIKE TERMS – PROBLEM #5
Simplify the following expression below. Combine like terms if possible.
𝟐𝒏 + 𝟔𝒃 + 𝟗𝒏 + 𝟐𝒃 + 𝒄
11n + 8b + c
LIKE TERMS – PROBLEM #6
Simplify the following expression below. Combine like terms if possible.
𝟐𝟑𝒈 − 𝟏𝟒𝒈 + 𝟓𝒇
9g + 5f
LIKE TERMS – PROBLEM #7
Simplify the following expression below. Combine like terms if possible.
𝟓(𝟑𝒏 + 𝟒)
15n + 20
REMEMBER: No symbol between 5 and the parenthesis
indicates a multiplication problem
LIKE TERMS – PROBLEM #8
Simplify the following expression below. Combine like terms if possible.
𝟒 𝟕𝒏 + 𝟐 + 𝟔28n + 8 + 6
28n + 14
REMEMBER: No symbol between 4 and the parenthesis
indicates a multiplication problem
LIKE TERMS – PROBLEM #9
Simplify the following expression below. Combine like terms if possible.
𝟑 𝟐𝒙 − 𝟓 − 𝟐𝒙6x – 15 – 2x
4x - 15
REMEMBER: No symbol between 3 and the parenthesis
indicates a multiplication problem
LIKE TERMS – PROBLEM #10
Simplify the following expression below. Combine like terms if possible.
𝟑 𝟒𝒙 − 𝟗𝒚 + 𝟓𝒙12x – 27y + 5x
17x – 27y
REMEMBER: No symbol between 3 and the parenthesis
indicates a multiplication problem
LIKE TERMS – PROBLEM #11
Simplify the following expression below. Combine like terms if possible.
𝟔 𝒂 + 𝟑 + 𝟕𝒙
6a + 18 + 7x
REMEMBER: No symbol between 6 and the parenthesis
indicates a multiplication problem
LIKE TERMS – PROBLEM #12
Simplify the following expression below. Combine like terms if possible.
𝟓 𝟐𝒏 + 𝟓𝒑 + 𝟔𝒏 + 𝟑𝒑 + 𝟖10n + 25p + 6n + 3p + 8
16n + 28p + 8
LIKE TERMS – PROBLEM #13
Simplify the following expression below. Combine like terms if possible.
𝟐 𝟐𝒃 + 𝟖 + 𝟖𝒃 − 𝟏𝟐𝒏 + 𝟏𝟒4b + 16 + 8b – 12n + 14
12b – 12n + 30
LIKE TERMS – PROBLEM #14
Simplify the following expression below. Combine like terms if possible.
𝟑 𝟓𝒈 + 𝟐𝒄 + 𝟓𝒈 − 𝟐𝒄 + 𝟑15g + 6c + 5g - 2c +3
20g + 4c + 3
LIKE TERMS – PROBLEM #15Simplify the following expression below. Combine like terms if
possible.
𝟐𝒙 + 𝟔(𝒙 + 𝟏)
2x + 6x + 68x + 6
Explain why each of the answers below would be incorrect for the above expression.
𝟐𝒙 + 𝟔𝒙 + 𝟏 𝒂𝒏𝒅 𝟗𝒙
*Didn’t multiply the 6 by the 1 * cannot add unlike terms
LIKE TERMS – PROBLEM #16
Simplify the following expression below. Combine like terms if possible.
𝟖 𝟓𝒈 + 𝟓 − 𝟐40g + 40 - 16
LIKE TERMS – PROBLEM #17
Simplify the following expression below. Combine like terms if possible.
𝟏𝟎(𝒏 + 𝟒 + 𝟖𝒎)10n + 40 + 80m