You’ve uploaded a worksheet titled
“Multiplying Polynomials”, and it asks you to multiply a monomial by a polynomial in each of the 8 problems. The key concept here is the
Distributive Property:
>
a(b + c + d) = ab + ac + ad
We’ll go through each problem one by one, distributing the monomial across each term inside the parentheses, then simplifying.
---
1) 3u²(3u³ + 5u – 7u⁵ + 12)
Distribute 3u² to each term:
- 3u² × 3u³ =
9u⁵
- 3u² × 5u =
15u³
- 3u² × (–7u⁵) =
–21u⁷
- 3u² × 12 =
36u²
Now write them in standard form (descending powers):
✔ Answer: –21u⁷ + 9u⁵ + 15u³ + 36u²
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2) –5x²(–4x⁶ + 8x⁴ + 10)
Distribute –5x²:
- –5x² × (–4x⁶) =
+20x⁸
- –5x² × 8x⁴ =
–40x⁶
- –5x² × 10 =
–50x²
✔ Answer: 20x⁸ – 40x⁶ – 50x²
---
3) 7a⁵(–4a³ – 6a⁷)
Distribute 7a⁵:
- 7a⁵ × (–4a³) =
–28a⁸
- 7a⁵ × (–6a⁷) =
–42a¹²
Write in descending order:
✔ Answer: –42a¹² – 28a⁸
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4) 9w(–2w³ + 6w⁵ – 7w²)
Distribute 9w:
- 9w × (–2w³) =
–18w⁴
- 9w × 6w⁵ =
54w⁶
- 9w × (–7w²) =
–63w³
Order by degree:
✔ Answer: 54w⁶ – 18w⁴ – 63w³
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5) –s⁶(1 + 17s⁶)
Distribute –s⁶:
- –s⁶ × 1 =
–s⁶
- –s⁶ × 17s⁶ =
–17s¹²
✔ Answer: –17s¹² – s⁶
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6) 8y³(y⁴ + 11)
Distribute 8y³:
- 8y³ × y⁴ =
8y⁷
- 8y³ × 11 =
88y³
✔ Answer: 8y⁷ + 88y³
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7) –b²(4b⁶ + 8b⁴ + 2b + 9)
Distribute –b²:
- –b² × 4b⁶ =
–4b⁸
- –b² × 8b⁴ =
–8b⁶
- –b² × 2b =
–2b³
- –b² × 9 =
–9b²
✔ Answer: –4b⁸ – 8b⁶ – 2b³ – 9b²
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8) 10(7m⁹ – 3 – m⁷)
Distribute 10:
- 10 × 7m⁹ =
70m⁹
- 10 × (–3) =
–30
- 10 × (–m⁷) =
–10m⁷
Order by degree:
✔ Answer: 70m⁹ – 10m⁷ – 30
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##
✔ Final Answers Summary:
1.
–21u⁷ + 9u⁵ + 15u³ + 36u²
2.
20x⁸ – 40x⁶ – 50x²
3.
–42a¹² – 28a⁸
4.
54w⁶ – 18w⁴ – 63w³
5.
–17s¹² – s⁶
6.
8y⁷ + 88y³
7.
–4b⁸ – 8b⁶ – 2b³ – 9b²
8.
70m⁹ – 10m⁷ – 30
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## 💡 Key Tips:
- Always distribute the monomial to
every term inside the parentheses.
- Multiply coefficients and add exponents when multiplying same bases: `x^a * x^b = x^(a+b)`
- Write final answer in
standard form (highest exponent first).
Let me know if you’d like to see any step broken down further!
Parent Tip: Review the logic above to help your child master the concept of multiply polynomials worksheet.
