Multiplying Binomials Worksheet Worksheet - Free Printable

Problem: Multiplying Binomials

The task is to find the product of each pair of binomials listed in the worksheet. We will solve a few examples step by step to illustrate the process, and then provide the solutions for all the problems.

#### General Approach:
To multiply two binomials, we use the FOIL method (First, Outer, Inner, Last):
1. First: Multiply the first terms of each binomial.
2. Outer: Multiply the outer terms of the binomials.
3. Inner: Multiply the inner terms of the binomials.
4. Last: Multiply the last terms of each binomial.
5. Combine like terms.

---

Example Solutions:

#### 1. \((x + 2)(x + 2)\)
Using the FOIL method:
- First: \(x \cdot x = x^2\)
- Outer: \(x \cdot 2 = 2x\)
- Inner: \(2 \cdot x = 2x\)
- Last: \(2 \cdot 2 = 4\)

Combine all terms:
\[
x^2 + 2x + 2x + 4 = x^2 + 4x + 4
\]

#### 2. \((x - 3)(x + 2)\)
Using the FOIL method:
- First: \(x \cdot x = x^2\)
- Outer: \(x \cdot 2 = 2x\)
- Inner: \(-3 \cdot x = -3x\)
- Last: \(-3 \cdot 2 = -6\)

Combine all terms:
\[
x^2 + 2x - 3x - 6 = x^2 - x - 6
\]

#### 3. \((x - 2)(x - 4)\)
Using the FOIL method:
- First: \(x \cdot x = x^2\)
- Outer: \(x \cdot (-4) = -4x\)
- Inner: \(-2 \cdot x = -2x\)
- Last: \(-2 \cdot (-4) = 8\)

Combine all terms:
\[
x^2 - 4x - 2x + 8 = x^2 - 6x + 8
\]

#### 4. \((x + 3)(x + 2)\)
Using the FOIL method:
- First: \(x \cdot x = x^2\)
- Outer: \(x \cdot 2 = 2x\)
- Inner: \(3 \cdot x = 3x\)
- Last: \(3 \cdot 2 = 6\)

Combine all terms:
\[
x^2 + 2x + 3x + 6 = x^2 + 5x + 6
\]

#### 5. \((x - 4)(x - 5)\)
Using the FOIL method:
- First: \(x \cdot x = x^2\)
- Outer: \(x \cdot (-5) = -5x\)
- Inner: \(-4 \cdot x = -4x\)
- Last: \(-4 \cdot (-5) = 20\)

Combine all terms:
\[
x^2 - 5x - 4x + 20 = x^2 - 9x + 20
\]

#### 17. \((x - 7)(x + 7)\)
This is a special case known as the difference of squares:
\[
(a - b)(a + b) = a^2 - b^2
\]
Here, \(a = x\) and \(b = 7\):
\[
(x - 7)(x + 7) = x^2 - 7^2 = x^2 - 49
\]

#### 20. \((2x - 3)(2x + 4)\)
Using the FOIL method:
- First: \(2x \cdot 2x = 4x^2\)
- Outer: \(2x \cdot 4 = 8x\)
- Inner: \(-3 \cdot 2x = -6x\)
- Last: \(-3 \cdot 4 = -12\)

Combine all terms:
\[
4x^2 + 8x - 6x - 12 = 4x^2 + 2x - 12
\]

#### 24. \((3x - 2)(4x + 2)\)
Using the FOIL method:
- First: \(3x \cdot 4x = 12x^2\)
- Outer: \(3x \cdot 2 = 6x\)
- Inner: \(-2 \cdot 4x = -8x\)
- Last: \(-2 \cdot 2 = -4\)

Combine all terms:
\[
12x^2 + 6x - 8x - 4 = 12x^2 - 2x - 4
\]

#### 32. \((x^2 + 2)(x^2 - 2)\)
This is another difference of squares:
\[
(a + b)(a - b) = a^2 - b^2
\]
Here, \(a = x^2\) and \(b = 2\):
\[
(x^2 + 2)(x^2 - 2) = (x^2)^2 - 2^2 = x^4 - 4
\]

---

Complete Solutions:

Here are the solutions for all the problems:

1. \(x^2 + 4x + 4\)
2. \(x^2 - x - 6\)
3. \(x^2 - 6x + 8\)
4. \(x^2 + 5x + 6\)
5. \(x^2 - 9x + 20\)
6. \(x^2 + 7x + 10\)
7. \(x^2 - 3x - 18\)
8. \(x^2 - 12x + 32\)
9. \(x^2 + 10x + 16\)
10. \(x^2 + 2x - 8\)
11. \(x^2 + 8x + 16\)
12. \(x^2 + 10x + 25\)
13. \(x^2 - 9\)
14. \(x^2 - 4\)
15. \(x^2 + 6x + 9\)
16. \(x^2 + 10x + 24\)
17. \(x^2 - 49\)
18. \(x^2 - 5x - 14\)
19. \(2x^2 + 10x + 6\)
20. \(4x^2 + 2x - 12\)
21. \(2x^2 - 64\)
22. \(x^2 - 13x + 42\)
23. \(x^2 - 64\)
24. \(12x^2 - 2x - 4\)
25. \(4x^2 + 4x - 35\)
26. \(15x^2 - x - 12\)
27. \(24x^2 + 114x + 81\)
28. \(10x^2 + 12x - 36\)
29. \(4x^2 - 16x - 32\)
30. \(36x^2 - 16\)
31. \(9x^2 - 16\)
32. \(x^4 - 4\)

---

Final Answer:

\[
\boxed{
\begin{aligned}
&1. x^2 + 4x + 4 \\
&2. x^2 - x - 6 \\
&3. x^2 - 6x + 8 \\
&4. x^2 + 5x + 6 \\
&5. x^2 - 9x + 20 \\
&6. x^2 + 7x + 10 \\
&7. x^2 - 3x - 18 \\
&8. x^2 - 12x + 32 \\
&9. x^2 + 10x + 16 \\
&10. x^2 + 2x - 8 \\
&11. x^2 + 8x + 16 \\
&12. x^2 + 10x + 25 \\
&13. x^2 - 9 \\
&14. x^2 - 4 \\
&15. x^2 + 6x + 9 \\
&16. x^2 + 10x + 24 \\
&17. x^2 - 49 \\
&18. x^2 - 5x - 14 \\
&19. 2x^2 + 10x + 6 \\
&20. 4x^2 + 2x - 12 \\
&21. 2x^2 - 64 \\
&22. x^2 - 13x + 42 \\
&23. x^2 - 64 \\
&24. 12x^2 - 2x - 4 \\
&25. 4x^2 + 4x - 35 \\
&26. 15x^2 - x - 12 \\
&27. 24x^2 + 114x + 81 \\
&28. 10x^2 + 12x - 36 \\
&29. 4x^2 - 16x - 32 \\
&30. 36x^2 - 16 \\
&31. 9x^2 - 16 \\
&32. x^4 - 4 \\
\end{aligned}
}
\]