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
Parent Tip: Review the logic above to help your child master the concept of multiplying algebraic expressions worksheet.