Simplify Algebraic Expressions By collecting like terms worksheet ... - Free Printable

Let's solve each expression by collecting like terms. Like terms are terms that have the same variable(s) raised to the same power. We combine them by adding or subtracting their coefficients.

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a) $ 2x + 6y + 7x $

- Like terms: $2x$ and $7x$
- Combine: $2x + 7x = 9x$
- $6y$ has no like term

✔ Answer: $9x + 6y$

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b) $ 3a + 8b + 5a $

- Like terms: $3a$ and $5a$
- Combine: $3a + 5a = 8a$
- $8b$ has no like term

✔ Answer: $8a + 8b$

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c) $ 6u + 3v - 2u $

- Like terms: $6u$ and $-2u$
- Combine: $6u - 2u = 4u$
- $3v$ has no like term

✔ Answer: $4u + 3v$

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d) $ 9p + 8q - p $

- Like terms: $9p$ and $-p$
- Combine: $9p - p = 8p$
- $8q$ has no like term

✔ Answer: $8p + 8q$

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e) $ 2m + 5n + 4m + 3n $

- Like terms:
- $2m + 4m = 6m$
- $5n + 3n = 8n$

✔ Answer: $6m + 8n$

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f) $ 6u + 9v + u + 3v $

- Like terms:
- $6u + u = 7u$
- $9v + 3v = 12v$

✔ Answer: $7u + 12v$

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g) $ 8b + 7c + 3b - 2c $

- Like terms:
- $8b + 3b = 11b$
- $7c - 2c = 5c$

✔ Answer: $11b + 5c$

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h) $ a + 2b + a - b $

- Like terms:
- $a + a = 2a$
- $2b - b = b$

✔ Answer: $2a + b$

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i) $ 5a + 2b - 5a + 6b $

- Like terms:
- $5a - 5a = 0$ (they cancel out)
- $2b + 6b = 8b$

✔ Answer: $8b$

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j) $ 9p + 3q - 2p - 3q $

- Like terms:
- $9p - 2p = 7p$
- $3q - 3q = 0$ (they cancel out)

✔ Answer: $7p$

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✔ Final Answers:

a) $9x + 6y$
b) $8a + 8b$
c) $4u + 3v$
d) $8p + 8q$
e) $6m + 8n$
f) $7u + 12v$
g) $11b + 5c$
h) $2a + b$
i) $8b$
j) $7p$

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