Let’s solve this matching problem step by step. We are given expressions on the left and their simplified or expanded forms on the right. Our goal is to match each expression on the left with its correct result on the right.
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1. 3xy × 4xy
Multiply coefficients: 3 × 4 = 12
Multiply variables: x × x = x², y × y = y²
→
12x²y²
✔ Match:
12x²y²
---
2. -3x²y × 4x
Coefficients: -3 × 4 = -12
Variables: x² × x = x³, y remains
→
-12x³y
✔ Match:
-12x³y
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3. 3x × (2 - 4y)
Distribute 3x:
3x × 2 = 6x
3x × (-4y) = -12xy
→
6x - 12xy
✔ Match:
6x - 12xy
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4. 4xy² × (-3y)
Coefficients: 4 × (-3) = -12
Variables: x remains, y² × y = y³
→
-12xy³
✔ Match:
-12xy³
---
5. 4y × (2x + 3)
Distribute 4y:
4y × 2x = 8xy
4y × 3 = 12y
→
8xy + 12y
✔ Match:
8xy + 12y
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6. 2x × 4y²
Coefficients: 2 × 4 = 8
Variables: x × y² = xy²
→
8xy²
✔ Match:
8xy²
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7. 5xy² + 2xy²
These are like terms (same variables and exponents).
Add coefficients: 5 + 2 = 7
→
7xy²
✔ Match:
7xy²
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8. 8x²y - 5x²y
Like terms again.
Subtract coefficients: 8 - 5 = 3
→
3x²y
✔ Match:
3x²y
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9. -5 × 2y
Multiply: -5 × 2 = -10, then × y
→
-10y
✔ Match:
-10y
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10. 2 + 4y + 5 - y
Combine like terms:
Constants: 2 + 5 = 7
y terms: 4y - y = 3y
→
3y + 7
✔ Match:
3y + 7
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##
✔ Final Matching:
| Left Expression | Right Result |
|-----------------------------|------------------|
| 3xy × 4xy | 12x²y² |
| -3x²y × 4x | -12x³y |
| 3x × (2 - 4y) | 6x - 12xy |
| 4xy² × -3y | -12xy³ |
| 4y × (2x + 3) | 8xy + 12y |
| 2x × 4y² | 8xy² |
| 5xy² + 2xy² | 7xy² |
| 8x²y - 5x²y | 3x²y |
| -5 × 2y | -10y |
| 2 + 4y + 5 - y | 3y + 7 |
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All matched correctly! 🎉
Parent Tip: Review the logic above to help your child master the concept of 8th grade algebra worksheet with answer key.
