You've uploaded a worksheet titled
“Multiplying a Polynomial and a Monomial” from Kuta Software — Infinite Pre-Algebra. The task is to
find each product, meaning you must distribute the monomial (the term outside the parentheses) to each term inside the polynomial (inside the parentheses).
This is an application of the
Distributive Property:
>
a(b + c) = ab + ac
We’ll go through each problem one by one, showing the steps.
---
1) 8x(6x + 6)
→ Distribute 8x to both terms:
= 8x·6x + 8x·6
=
48x² + 48x
---
2) 7n(6n + 3)
→ Distribute 7n:
= 7n·6n + 7n·3
=
42n² + 21n
---
3) 3r(7r − 8)
→ Distribute 3r:
= 3r·7r − 3r·8
=
21r² − 24r
---
4) 8(8k − 8)
→ Distribute 8:
= 8·8k − 8·8
=
64k − 64
---
5) 10a(a − 10b)
→ Distribute 10a:
= 10a·a − 10a·10b
=
10a² − 100ab
---
6) 2(9x − 2y)
→ Distribute 2:
= 2·9x − 2·2y
=
18x − 4y
---
7) 7x(6x + 4y)
→ Distribute 7x:
= 7x·6x + 7x·4y
=
42x² + 28xy
---
8) 4a(8a − 8b)
→ Distribute 4a:
= 4a·8a − 4a·8b
=
32a² − 32ab
---
9) 3m(m² − 6m + 5)
→ Distribute 3m:
= 3m·m² − 3m·6m + 3m·5
=
3m³ − 18m² + 15m
---
10) 2k³(2k² + 5k − 4)
→ Distribute 2k³:
= 2k³·2k² + 2k³·5k − 2k³·4
=
4k⁵ + 10k⁴ − 8k³
---
11) 8r²(4r² − 5r + 7)
→ Distribute 8r²:
= 8r²·4r² − 8r²·5r + 8r²·7
=
32r⁴ − 40r³ + 56r²
---
12) 3(3x² + 8x − 5)
→ Distribute 3:
= 3·3x² + 3·8x − 3·5
=
9x² + 24x − 15
---
13) 7(6x² + 9xy + 10y²)
→ Distribute 7:
= 7·6x² + 7·9xy + 7·10y²
=
42x² + 63xy + 70y²
---
14) 2a(6u² − 9uv + v²)
→ Distribute 2a:
= 2a·6u² − 2a·9uv + 2a·v²
=
12au² − 18auv + 2av²
---
15) 9(x² + xy − 8y²)
→ Distribute 9:
= 9·x² + 9·xy − 9·8y²
=
9x² + 9xy − 72y²
---
16) 9v²(u² + uv − 5v²)
→ Distribute 9v²:
= 9v²·u² + 9v²·uv − 9v²·5v²
=
9u²v² + 9uv³ − 45v⁴
*(Note: When multiplying variables with exponents, add the exponents if bases are same: e.g., v²·v = v³, v²·v² = v⁴)*
---
##
✔ Final Answers:
1)
48x² + 48x
2)
42n² + 21n
3)
21r² − 24r
4)
64k − 64
5)
10a² − 100ab
6)
18x − 4y
7)
42x² + 28xy
8)
32a² − 32ab
9)
3m³ − 18m² + 15m
10)
4k⁵ + 10k⁴ − 8k³
11)
32r⁴ − 40r³ + 56r²
12)
9x² + 24x − 15
13)
42x² + 63xy + 70y²
14)
12au² − 18auv + 2av²
15)
9x² + 9xy − 72y²
16)
9u²v² + 9uv³ − 45v⁴
---
## 💡 Key Concepts:
-
Distributive Property: Multiply the monomial by *each* term in the polynomial.
-
Exponent Rules: When multiplying same bases, add exponents: xᵃ·xᵇ = xᵃ⁺ᵇ.
-
Combine Like Terms? Not needed here — since we’re distributing, we just simplify each product.
Let me know if you’d like a printable answer key or step-by-step video explanation for any problem!
Parent Tip: Review the logic above to help your child master the concept of monomials worksheet.
