Worksheets for simplifying expressions - Free Printable

To solve the given worksheet, we will simplify each expression step by step. Let's go through each problem:

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1a. \( 6y - 2y \)

- Combine like terms:
\[
6y - 2y = (6 - 2)y = 4y
\]
- Answer: \( 4y \)

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1b. \( 6 - 7b + 7b + 3 + b \)

- Combine like terms:
- Constants: \( 6 + 3 = 9 \)
- Variables: \( -7b + 7b + b = 0b + b = b \)
- Simplified expression: \( 9 + b \)
- Answer: \( 9 + b \)

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2a. \( 10a - 2 + 3 - a \)

- Combine like terms:
- Variables: \( 10a - a = 9a \)
- Constants: \( -2 + 3 = 1 \)
- Simplified expression: \( 9a + 1 \)
- Answer: \( 9a + 1 \)

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2b. \( m \cdot 7 \cdot m \cdot m \cdot m \cdot 9 \)

- Rearrange and combine coefficients and variables:
- Coefficients: \( 7 \cdot 9 = 63 \)
- Variables: \( m \cdot m \cdot m \cdot m = m^4 \)
- Simplified expression: \( 63m^4 \)
- Answer: \( 63m^4 \)

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3a. \( 3 + 8(5a + 10) \)

- Distribute the 8 inside the parentheses:
\[
8(5a + 10) = 8 \cdot 5a + 8 \cdot 10 = 40a + 80
\]
- Add the constant term:
\[
3 + 40a + 80 = 40a + 83
\]
- Answer: \( 40a + 83 \)

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3b. \( 6v - 8v + 4 + 6v \)

- Combine like terms:
- Variables: \( 6v - 8v + 6v = (6 - 8 + 6)v = 4v \)
- Constants: \( 4 \)
- Simplified expression: \( 4v + 4 \)
- Answer: \( 4v + 4 \)

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4a. \( s \cdot 1 \cdot s \cdot 3 \)

- Simplify the multiplication:
- Coefficient: \( 1 \cdot 3 = 3 \)
- Variables: \( s \cdot s = s^2 \)
- Simplified expression: \( 3s^2 \)
- Answer: \( 3s^2 \)

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4b. \( 6k - 6k \)

- Combine like terms:
\[
6k - 6k = 0
\]
- Answer: \( 0 \)

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5a. \( 10y^4 \cdot y^2 \)

- Use the property of exponents \( a^m \cdot a^n = a^{m+n} \):
\[
10y^4 \cdot y^2 = 10y^{4+2} = 10y^6
\]
- Answer: \( 10y^6 \)

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5b. \( 10x + 7 - 5x \)

- Combine like terms:
- Variables: \( 10x - 5x = 5x \)
- Constants: \( 7 \)
- Simplified expression: \( 5x + 7 \)
- Answer: \( 5x + 7 \)

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6a. \( 1v - v + 7 + 9v \)

- Combine like terms:
- Variables: \( 1v - v + 9v = (1 - 1 + 9)v = 9v \)
- Constants: \( 7 \)
- Simplified expression: \( 9v + 7 \)
- Answer: \( 9v + 7 \)

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6b. \( 6z - 5 + 5 - 6z \)

- Combine like terms:
- Variables: \( 6z - 6z = 0 \)
- Constants: \( -5 + 5 = 0 \)
- Simplified expression: \( 0 \)
- Answer: \( 0 \)

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7a. \( 9w + 5w \)

- Combine like terms:
\[
9w + 5w = (9 + 5)w = 14w
\]
- Answer: \( 14w \)

---

7b. \( s \cdot 2s \cdot s \cdot s \cdot s \)

- Simplify the multiplication:
- Coefficient: \( 1 \cdot 2 = 2 \)
- Variables: \( s \cdot s \cdot s \cdot s \cdot s = s^5 \)
- Simplified expression: \( 2s^5 \)
- Answer: \( 2s^5 \)

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Final Answer Key

\[
\boxed{
\begin{array}{ll}
1a. & 4y \\
1b. & 9 + b \\
2a. & 9a + 1 \\
2b. & 63m^4 \\
3a. & 40a + 83 \\
3b. & 4v + 4 \\
4a. & 3s^2 \\
4b. & 0 \\
5a. & 10y^6 \\
5b. & 5x + 7 \\
6a. & 9v + 7 \\
6b. & 0 \\
7a. & 14w \\
7b. & 2s^5 \\
\end{array}
}
\]