Multiplying a Polynomial and a Monomial worksheets - Free Printable

Problem: Multiplying a Polynomial and a Monomial

The task is to find the product of each given expression by distributing the monomial across the terms in the polynomial. This involves applying the distributive property, which states:

\[
a(b + c) = ab + ac
\]

We will solve each problem step by step.

---

Solutions:

#### 1. \( 13(x + 3) \)
\[
13(x + 3) = 13 \cdot x + 13 \cdot 3 = 13x + 39
\]

#### 2. \( 20x(x - 4y) \)
\[
20x(x - 4y) = 20x \cdot x + 20x \cdot (-4y) = 20x^2 - 80xy
\]

#### 3. \( 14(x + 2) \)
\[
14(x + 2) = 14 \cdot x + 14 \cdot 2 = 14x + 28
\]

#### 4. \( 16(x + 4) \)
\[
16(x + 4) = 16 \cdot x + 16 \cdot 4 = 16x + 64
\]

#### 5. \( 18x(x - 2y) \)
\[
18x(x - 2y) = 18x \cdot x + 18x \cdot (-2y) = 18x^2 - 36xy
\]

#### 6. \( 8x(x - 4y) \)
\[
8x(x - 4y) = 8x \cdot x + 8x \cdot (-4y) = 8x^2 - 32xy
\]

#### 7. \( -12x(x + 3) \)
\[
-12x(x + 3) = -12x \cdot x + (-12x) \cdot 3 = -12x^2 - 36x
\]

#### 8. \( 10x(x - 3y) \)
\[
10x(x - 3y) = 10x \cdot x + 10x \cdot (-3y) = 10x^2 - 30xy
\]

#### 9. \( -7x(x + 4) \)
\[
-7x(x + 4) = -7x \cdot x + (-7x) \cdot 4 = -7x^2 - 28x
\]

#### 10. \( 15x(x - 2y) \)
\[
15x(x - 2y) = 15x \cdot x + 15x \cdot (-2y) = 15x^2 - 30xy
\]

#### 11. \( 16x(x - 3y + 8) \)
\[
16x(x - 3y + 8) = 16x \cdot x + 16x \cdot (-3y) + 16x \cdot 8 = 16x^2 - 48xy + 128x
\]

#### 12. \( 11(x + 3) \)
\[
11(x + 3) = 11 \cdot x + 11 \cdot 3 = 11x + 33
\]

#### 13. \( 9x(x - 2y + 5) \)
\[
9x(x - 2y + 5) = 9x \cdot x + 9x \cdot (-2y) + 9x \cdot 5 = 9x^2 - 18xy + 45x
\]

#### 14. \( -4x(x + 4) \)
\[
-4x(x + 4) = -4x \cdot x + (-4x) \cdot 4 = -4x^2 - 16x
\]

#### 15. \( 13x(x - 2y + 7) \)
\[
13x(x - 2y + 7) = 13x \cdot x + 13x \cdot (-2y) + 13x \cdot 7 = 13x^2 - 26xy + 91x
\]

#### 16. \( 21(x + 3) \)
\[
21(x + 3) = 21 \cdot x + 21 \cdot 3 = 21x + 63
\]

#### 17. \( -10x(x + 4) \)
\[
-10x(x + 4) = -10x \cdot x + (-10x) \cdot 4 = -10x^2 - 40x
\]

#### 18. \( 14x(x - 3y) \)
\[
14x(x - 3y) = 14x \cdot x + 14x \cdot (-3y) = 14x^2 - 42xy
\]

#### 19. \( 7x(x - 4y) \)
\[
7x(x - 4y) = 7x \cdot x + 7x \cdot (-4y) = 7x^2 - 28xy
\]

#### 20. \( -11x(x + 4) \)
\[
-11x(x + 4) = -11x \cdot x + (-11x) \cdot 4 = -11x^2 - 44x
\]

#### 21. \( -15x(x + 4) \)
\[
-15x(x + 4) = -15x \cdot x + (-15x) \cdot 4 = -15x^2 - 60x
\]

#### 22. \( 17x(x - 4y) \)
\[
17x(x - 4y) = 17x \cdot x + 17x \cdot (-4y) = 17x^2 - 68xy
\]

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 13x + 39 \\
2. & \ 20x^2 - 80xy \\
3. & \ 14x + 28 \\
4. & \ 16x + 64 \\
5. & \ 18x^2 - 36xy \\
6. & \ 8x^2 - 32xy \\
7. & \ -12x^2 - 36x \\
8. & \ 10x^2 - 30xy \\
9. & \ -7x^2 - 28x \\
10. & \ 15x^2 - 30xy \\
11. & \ 16x^2 - 48xy + 128x \\
12. & \ 11x + 33 \\
13. & \ 9x^2 - 18xy + 45x \\
14. & \ -4x^2 - 16x \\
15. & \ 13x^2 - 26xy + 91x \\
16. & \ 21x + 63 \\
17. & \ -10x^2 - 40x \\
18. & \ 14x^2 - 42xy \\
19. & \ 7x^2 - 28xy \\
20. & \ -11x^2 - 44x \\
21. & \ -15x^2 - 60x \\
22. & \ 17x^2 - 68xy \\
\end{aligned}
}
\]