Simplify Expressions Worksheets with algebraic multiplication exercises.

Let’s solve each expression step by step. We’ll multiply the numbers first, then combine the variables (letters) using exponent rules: when you multiply same bases, add exponents.

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Left Column:

1. 5x × 2x × 3y
Numbers: 5 × 2 × 3 = 30
Variables: x × x = x², and y stays → so x²y
→ 30x²y

2. 2 × 2 × 3x × 4
Numbers: 2 × 2 × 3 × 4 = 48
Only one variable: x
→ 48x

3. 2a × 3ab × 2c
Numbers: 2 × 3 × 2 = 12
Variables: a × a = a², b, c → so a²bc
→ 12a²bc

4. 9 × x² × xy
Numbers: 9
Variables: x² × x = x³, and y → so x³y
→ 9x³y

5. 4xy × 2x²y × 7
Numbers: 4 × 2 × 7 = 56
Variables: x × x² = x³, y × y = y² → so x³y²
→ 56x³y²

6. 9x × 2xy × 3x²
Numbers: 9 × 2 × 3 = 54
Variables: x × x = x², times x² = x⁴, and y → so x⁴y
→ 54x⁴y

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Right Column:

7. 2x × 3y × 2xy
Numbers: 2 × 3 × 2 = 12
Variables: x × x = x², y × y = y² → so x²y²
→ 12x²y²

8. 4 × 2x × 3x²y
Numbers: 4 × 2 × 3 = 24
Variables: x × x² = x³, and y → so x³y
→ 24x³y

9. 10x × 2y × 3
Numbers: 10 × 2 × 3 = 60
Variables: x and y → so xy
→ 60xy

10. 4xy² × 2x²y
Numbers: 4 × 2 = 8
Variables: x × x² = x³, y² × y = y³ → so x³y³
→ 8x³y³

11. 9 × xyz × 4xy
Numbers: 9 × 4 = 36
Variables: x × x = x², y × y = y², z → so x²y²z
→ 36x²y²z

12. 2x × xy² × 3xy
Numbers: 2 × 3 = 6
Variables: x × x = x², times x = x³; y² × y = y³ → so x³y³
→ 6x³y³

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Final Answer:

Left Column:
1. 30x²y
2. 48x
3. 12a²bc
4. 9x³y
5. 56x³y²
6. 54x⁴y

Right Column:
7. 12x²y²
8. 24x³y
9. 60xy
10. 8x³y³
11. 36x²y²z
12. 6x³y³