To solve these problems, we need to combine "like terms." Like terms are parts of an expression that have the same variable (letter) raised to the same power. We can add or subtract their coefficients (the numbers in front). Constants (just numbers with no variables) can also be combined with other constants.
Let’s go through each one:
1)
8n - n
Think of “n” as “1n”. So this is 8n - 1n = 7n.
2)
-6 + 8n + 9 - 7n
Group like terms:
Constants: -6 + 9 = 3
Variables: 8n - 7n = 1n → just n
Answer: 3 + n (or n + 3 — both are correct)
3)
c + 3c
c is the same as 1c, so 1c + 3c = 4c
4)
4r - 5r
4 - 5 = -1, so answer is -1r → just -r
5)
3p + p
p is 1p, so 3p + 1p = 4p
6)
9r + 3r + 4
Combine r terms: 9r + 3r = 12r
Constant stays: +4
Answer: 12r + 4
7)
4z + 9 + 5z - 2
z terms: 4z + 5z = 9z
Constants: 9 - 2 = 7
Answer: 9z + 7
8)
5 - 4m - 9
Constants: 5 - 9 = -4
Variable: -4m stays
Answer: -4m - 4
9)
7 + 4s + 9
Constants: 7 + 9 = 16
Variable: 4s stays
Answer: 4s + 16
10)
-7n + 8 + 6 + 2n
n terms: -7n + 2n = -5n
Constants: 8 + 6 = 14
Answer: -5n + 14
All answers checked and verified.
Final Answer:
1) 7n
2) n + 3
3) 4c
4) -r
5) 4p
6) 12r + 4
7) 9z + 7
8) -4m - 4
9) 4s + 16
10) -5n + 14
Parent Tip: Review the logic above to help your child master the concept of combining like terms algebra 1 worksheet.
