Algebra worksheet for practicing combining like terms.
A worksheet titled "Combining Like Terms" with 26 algebraic expressions to simplify, presented in a clear, structured format with numbered problems.
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Step-by-step solution for: Combining Like Terms #1 | Worksheet | Combining ...
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Show Answer Key & Explanations
Step-by-step solution for: Combining Like Terms #1 | Worksheet | Combining ...
To solve these problems, we need to combine "like terms." Like terms are terms that have the same variable raised to the same power. For example, $x$ and $2x$ are like terms, and $x^2$ and $3x^2$ are like terms. We just add or subtract their coefficients (the numbers in front).
Let's go through each problem one by one:
1. $x + 2x$
* Combine $1x$ and $2x$: $1 + 2 = 3$.
* Result: $3x$
2. $2x - x$
* Combine $2x$ and $-1x$: $2 - 1 = 1$.
* Result: $x$
3. $4x + 2x$
* Combine $4x$ and $2x$: $4 + 2 = 6$.
* Result: $6x$
4. $6x - 3x$
* Combine $6x$ and $-3x$: $6 - 3 = 3$.
* Result: $3x$
5. $5x + x$
* Combine $5x$ and $1x$: $5 + 1 = 6$.
* Result: $6x$
6. $2x + 2x$
* Combine $2x$ and $2x$: $2 + 2 = 4$.
* Result: $4x$
7. $7x - 5x$
* Combine $7x$ and $-5x$: $7 - 5 = 2$.
* Result: $2x$
8. $3x - 2x$
* Combine $3x$ and $-2x$: $3 - 2 = 1$.
* Result: $x$
9. $x + x$
* Combine $1x$ and $1x$: $1 + 1 = 2$.
* Result: $2x$
10. $x^2 + 2x^2$
* Combine $1x^2$ and $2x^2$: $1 + 2 = 3$.
* Result: $3x^2$
11. $4x^2 - 3x^2$
* Combine $4x^2$ and $-3x^2$: $4 - 3 = 1$.
* Result: $x^2$
12. $3x^2 + 2x^2$
* Combine $3x^2$ and $2x^2$: $3 + 2 = 5$.
* Result: $5x^2$
13. $2x^2 + 2x + x^2 + x$
* Group like terms: $(2x^2 + x^2) + (2x + x)$.
* Combine $x^2$ terms: $2 + 1 = 3 \rightarrow 3x^2$.
* Combine $x$ terms: $2 + 1 = 3 \rightarrow 3x$.
* Result: $3x^2 + 3x$
14. $5x + x^2 - 2x + x^2$
* Group like terms: $(x^2 + x^2) + (5x - 2x)$.
* Combine $x^2$ terms: $1 + 1 = 2 \rightarrow 2x^2$.
* Combine $x$ terms: $5 - 2 = 3 \rightarrow 3x$.
* Result: $2x^2 + 3x$
15. $3x + 2x - x + 2x^2$
* Group like terms: $2x^2 + (3x + 2x - x)$.
* Combine $x$ terms: $3 + 2 - 1 = 4 \rightarrow 4x$.
* Result: $2x^2 + 4x$
16. $6x + 3x^2 - x - x^2$
* Group like terms: $(3x^2 - x^2) + (6x - x)$.
* Combine $x^2$ terms: $3 - 1 = 2 \rightarrow 2x^2$.
* Combine $x$ terms: $6 - 1 = 5 \rightarrow 5x$.
* Result: $2x^2 + 5x$
17. $4x + 3 + x^2 - x$
* Group like terms: $x^2 + (4x - x) + 3$.
* Combine $x$ terms: $4 - 1 = 3 \rightarrow 3x$.
* Result: $x^2 + 3x + 3$
18. $2x + 3x + 9 + x$
* Group like terms: $(2x + 3x + x) + 9$.
* Combine $x$ terms: $2 + 3 + 1 = 6 \rightarrow 6x$.
* Result: $6x + 9$
19. $2x^2 + 3 + 3x - 1$
* Group like terms: $2x^2 + 3x + (3 - 1)$.
* Combine constants: $3 - 1 = 2$.
* Result: $2x^2 + 3x + 2$
20. $2x + 5 + x^2 - x$
* Group like terms: $x^2 + (2x - x) + 5$.
* Combine $x$ terms: $2 - 1 = 1 \rightarrow x$.
* Result: $x^2 + x + 5$
21. $2x + 4y - x + y$
* Group like terms: $(2x - x) + (4y + y)$.
* Combine $x$ terms: $2 - 1 = 1 \rightarrow x$.
* Combine $y$ terms: $4 + 1 = 5 \rightarrow 5y$.
* Result: $x + 5y$
22. $2y + x + 3x - y$
* Group like terms: $(x + 3x) + (2y - y)$.
* Combine $x$ terms: $1 + 3 = 4 \rightarrow 4x$.
* Combine $y$ terms: $2 - 1 = 1 \rightarrow y$.
* Result: $4x + y$
23. $x + y + 2y - 4$
* Group like terms: $x + (y + 2y) - 4$.
* Combine $y$ terms: $1 + 2 = 3 \rightarrow 3y$.
* Result: $x + 3y - 4$
24. $5 + 2x + y + 2x - 1$
* Group like terms: $(2x + 2x) + y + (5 - 1)$.
* Combine $x$ terms: $2 + 2 = 4 \rightarrow 4x$.
* Combine constants: $5 - 1 = 4$.
* Result: $4x + y + 4$
25. $3y + 2 + 2y + 5$
* Group like terms: $(3y + 2y) + (2 + 5)$.
* Combine $y$ terms: $3 + 2 = 5 \rightarrow 5y$.
* Combine constants: $2 + 5 = 7$.
* Result: $5y + 7$
26. $2x + 2y + x^2 - x + x^2$
* Group like terms: $(x^2 + x^2) + (2x - x) + 2y$.
* Combine $x^2$ terms: $1 + 1 = 2 \rightarrow 2x^2$.
* Combine $x$ terms: $2 - 1 = 1 \rightarrow x$.
* Result: $2x^2 + x + 2y$
Final Answer:
1) $3x$
2) $x$
3) $6x$
4) $3x$
5) $6x$
6) $4x$
7) $2x$
8) $x$
9) $2x$
10) $3x^2$
11) $x^2$
12) $5x^2$
13) $3x^2 + 3x$
14) $2x^2 + 3x$
15) $2x^2 + 4x$
16) $2x^2 + 5x$
17) $x^2 + 3x + 3$
18) $6x + 9$
19) $2x^2 + 3x + 2$
20) $x^2 + x + 5$
21) $x + 5y$
22) $4x + y$
23) $x + 3y - 4$
24) $4x + y + 4$
25) $5y + 7$
26) $2x^2 + x + 2y$
Let's go through each problem one by one:
1. $x + 2x$
* Combine $1x$ and $2x$: $1 + 2 = 3$.
* Result: $3x$
2. $2x - x$
* Combine $2x$ and $-1x$: $2 - 1 = 1$.
* Result: $x$
3. $4x + 2x$
* Combine $4x$ and $2x$: $4 + 2 = 6$.
* Result: $6x$
4. $6x - 3x$
* Combine $6x$ and $-3x$: $6 - 3 = 3$.
* Result: $3x$
5. $5x + x$
* Combine $5x$ and $1x$: $5 + 1 = 6$.
* Result: $6x$
6. $2x + 2x$
* Combine $2x$ and $2x$: $2 + 2 = 4$.
* Result: $4x$
7. $7x - 5x$
* Combine $7x$ and $-5x$: $7 - 5 = 2$.
* Result: $2x$
8. $3x - 2x$
* Combine $3x$ and $-2x$: $3 - 2 = 1$.
* Result: $x$
9. $x + x$
* Combine $1x$ and $1x$: $1 + 1 = 2$.
* Result: $2x$
10. $x^2 + 2x^2$
* Combine $1x^2$ and $2x^2$: $1 + 2 = 3$.
* Result: $3x^2$
11. $4x^2 - 3x^2$
* Combine $4x^2$ and $-3x^2$: $4 - 3 = 1$.
* Result: $x^2$
12. $3x^2 + 2x^2$
* Combine $3x^2$ and $2x^2$: $3 + 2 = 5$.
* Result: $5x^2$
13. $2x^2 + 2x + x^2 + x$
* Group like terms: $(2x^2 + x^2) + (2x + x)$.
* Combine $x^2$ terms: $2 + 1 = 3 \rightarrow 3x^2$.
* Combine $x$ terms: $2 + 1 = 3 \rightarrow 3x$.
* Result: $3x^2 + 3x$
14. $5x + x^2 - 2x + x^2$
* Group like terms: $(x^2 + x^2) + (5x - 2x)$.
* Combine $x^2$ terms: $1 + 1 = 2 \rightarrow 2x^2$.
* Combine $x$ terms: $5 - 2 = 3 \rightarrow 3x$.
* Result: $2x^2 + 3x$
15. $3x + 2x - x + 2x^2$
* Group like terms: $2x^2 + (3x + 2x - x)$.
* Combine $x$ terms: $3 + 2 - 1 = 4 \rightarrow 4x$.
* Result: $2x^2 + 4x$
16. $6x + 3x^2 - x - x^2$
* Group like terms: $(3x^2 - x^2) + (6x - x)$.
* Combine $x^2$ terms: $3 - 1 = 2 \rightarrow 2x^2$.
* Combine $x$ terms: $6 - 1 = 5 \rightarrow 5x$.
* Result: $2x^2 + 5x$
17. $4x + 3 + x^2 - x$
* Group like terms: $x^2 + (4x - x) + 3$.
* Combine $x$ terms: $4 - 1 = 3 \rightarrow 3x$.
* Result: $x^2 + 3x + 3$
18. $2x + 3x + 9 + x$
* Group like terms: $(2x + 3x + x) + 9$.
* Combine $x$ terms: $2 + 3 + 1 = 6 \rightarrow 6x$.
* Result: $6x + 9$
19. $2x^2 + 3 + 3x - 1$
* Group like terms: $2x^2 + 3x + (3 - 1)$.
* Combine constants: $3 - 1 = 2$.
* Result: $2x^2 + 3x + 2$
20. $2x + 5 + x^2 - x$
* Group like terms: $x^2 + (2x - x) + 5$.
* Combine $x$ terms: $2 - 1 = 1 \rightarrow x$.
* Result: $x^2 + x + 5$
21. $2x + 4y - x + y$
* Group like terms: $(2x - x) + (4y + y)$.
* Combine $x$ terms: $2 - 1 = 1 \rightarrow x$.
* Combine $y$ terms: $4 + 1 = 5 \rightarrow 5y$.
* Result: $x + 5y$
22. $2y + x + 3x - y$
* Group like terms: $(x + 3x) + (2y - y)$.
* Combine $x$ terms: $1 + 3 = 4 \rightarrow 4x$.
* Combine $y$ terms: $2 - 1 = 1 \rightarrow y$.
* Result: $4x + y$
23. $x + y + 2y - 4$
* Group like terms: $x + (y + 2y) - 4$.
* Combine $y$ terms: $1 + 2 = 3 \rightarrow 3y$.
* Result: $x + 3y - 4$
24. $5 + 2x + y + 2x - 1$
* Group like terms: $(2x + 2x) + y + (5 - 1)$.
* Combine $x$ terms: $2 + 2 = 4 \rightarrow 4x$.
* Combine constants: $5 - 1 = 4$.
* Result: $4x + y + 4$
25. $3y + 2 + 2y + 5$
* Group like terms: $(3y + 2y) + (2 + 5)$.
* Combine $y$ terms: $3 + 2 = 5 \rightarrow 5y$.
* Combine constants: $2 + 5 = 7$.
* Result: $5y + 7$
26. $2x + 2y + x^2 - x + x^2$
* Group like terms: $(x^2 + x^2) + (2x - x) + 2y$.
* Combine $x^2$ terms: $1 + 1 = 2 \rightarrow 2x^2$.
* Combine $x$ terms: $2 - 1 = 1 \rightarrow x$.
* Result: $2x^2 + x + 2y$
Final Answer:
1) $3x$
2) $x$
3) $6x$
4) $3x$
5) $6x$
6) $4x$
7) $2x$
8) $x$
9) $2x$
10) $3x^2$
11) $x^2$
12) $5x^2$
13) $3x^2 + 3x$
14) $2x^2 + 3x$
15) $2x^2 + 4x$
16) $2x^2 + 5x$
17) $x^2 + 3x + 3$
18) $6x + 9$
19) $2x^2 + 3x + 2$
20) $x^2 + x + 5$
21) $x + 5y$
22) $4x + y$
23) $x + 3y - 4$
24) $4x + y + 4$
25) $5y + 7$
26) $2x^2 + x + 2y$
Parent Tip: Review the logic above to help your child master the concept of combining like terms printable worksheet.
