Multiply the Binomials Worksheet 4 Worksheets - Free Printable

Problem Description:

The task is to multiply binomials using the FOIL method. The FOIL method stands for:
- F: First terms
- O: Outer terms
- I: Inner terms
- L: Last terms

We will apply this method to each of the given binomial multiplication problems.

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Solution:

#### 1. $(x - 2)(3x + 3)$

Using FOIL:
- F: $x \cdot 3x = 3x^2$
- O: $x \cdot 3 = 3x$
- I: $-2 \cdot 3x = -6x$
- L: $-2 \cdot 3 = -6$

Combine all terms:
$$
3x^2 + 3x - 6x - 6 = 3x^2 - 3x - 6
$$

Answer: $\boxed{3x^2 - 3x - 6}$

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#### 2. $(3x - 2)(4x + 1)$

Using FOIL:
- F: $3x \cdot 4x = 12x^2$
- O: $3x \cdot 1 = 3x$
- I: $-2 \cdot 4x = -8x$
- L: $-2 \cdot 1 = -2$

Combine all terms:
$$
12x^2 + 3x - 8x - 2 = 12x^2 - 5x - 2
$$

Answer: $\boxed{12x^2 - 5x - 2}$

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#### 3. $(4x - 1)(x - 2)$

Using FOIL:
- F: $4x \cdot x = 4x^2$
- O: $4x \cdot (-2) = -8x$
- I: $-1 \cdot x = -x$
- L: $-1 \cdot (-2) = 2$

Combine all terms:
$$
4x^2 - 8x - x + 2 = 4x^2 - 9x + 2
$$

Answer: $\boxed{4x^2 - 9x + 2}$

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#### 4. $(x - 2)(4x + 1)$

Using FOIL:
- F: $x \cdot 4x = 4x^2$
- O: $x \cdot 1 = x$
- I: $-2 \cdot 4x = -8x$
- L: $-2 \cdot 1 = -2$

Combine all terms:
$$
4x^2 + x - 8x - 2 = 4x^2 - 7x - 2
$$

Answer: $\boxed{4x^2 - 7x - 2}$

---

#### 5. $(2x + 4)(3x + 2)$

Using FOIL:
- F: $2x \cdot 3x = 6x^2$
- O: $2x \cdot 2 = 4x$
- I: $4 \cdot 3x = 12x$
- L: $4 \cdot 2 = 8$

Combine all terms:
$$
6x^2 + 4x + 12x + 8 = 6x^2 + 16x + 8
$$

Answer: $\boxed{6x^2 + 16x + 8}$

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#### 6. $(2x - 1)(2x - 5)$

Using FOIL:
- F: $2x \cdot 2x = 4x^2$
- O: $2x \cdot (-5) = -10x$
- I: $-1 \cdot 2x = -2x$
- L: $-1 \cdot (-5) = 5$

Combine all terms:
$$
4x^2 - 10x - 2x + 5 = 4x^2 - 12x + 5
$$

Answer: $\boxed{4x^2 - 12x + 5}$

---

#### 7. $(x - 5)(x - 3)$

Using FOIL:
- F: $x \cdot x = x^2$
- O: $x \cdot (-3) = -3x$
- I: $-5 \cdot x = -5x$
- L: $-5 \cdot (-3) = 15$

Combine all terms:
$$
x^2 - 3x - 5x + 15 = x^2 - 8x + 15
$$

Answer: $\boxed{x^2 - 8x + 15}$

---

#### 8. $(3x + 1)(x + 2)$

Using FOIL:
- F: $3x \cdot x = 3x^2$
- O: $3x \cdot 2 = 6x$
- I: $1 \cdot x = x$
- L: $1 \cdot 2 = 2$

Combine all terms:
$$
3x^2 + 6x + x + 2 = 3x^2 + 7x + 2
$$

Answer: $\boxed{3x^2 + 7x + 2}$

---

#### 9. $(n + 5)(5n + 2)$

Using FOIL:
- F: $n \cdot 5n = 5n^2$
- O: $n \cdot 2 = 2n$
- I: $5 \cdot 5n = 25n$
- L: $5 \cdot 2 = 10$

Combine all terms:
$$
5n^2 + 2n + 25n + 10 = 5n^2 + 27n + 10
$$

Answer: $\boxed{5n^2 + 27n + 10}$

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#### 10. $(x + 4)(4x - 2)$

Using FOIL:
- F: $x \cdot 4x = 4x^2$
- O: $x \cdot (-2) = -2x$
- I: $4 \cdot 4x = 16x$
- L: $4 \cdot (-2) = -8$

Combine all terms:
$$
4x^2 - 2x + 16x - 8 = 4x^2 + 14x - 8
$$

Answer: $\boxed{4x^2 + 14x - 8}$

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Final Answers:

1. $\boxed{3x^2 - 3x - 6}$
2. $\boxed{12x^2 - 5x - 2}$
3. $\boxed{4x^2 - 9x + 2}$
4. $\boxed{4x^2 - 7x - 2}$
5. $\boxed{6x^2 + 16x + 8}$
6. $\boxed{4x^2 - 12x + 5}$
7. $\boxed{x^2 - 8x + 15}$
8. $\boxed{3x^2 + 7x + 2}$
9. $\boxed{5n^2 + 27n + 10}$
10. $\boxed{4x^2 + 14x - 8}$

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Boxed Final Answer:

$$
\boxed{
\begin{aligned}
1. & \ 3x^2 - 3x - 6 \\
2. & \ 12x^2 - 5x - 2 \\
3. & \ 4x^2 - 9x + 2 \\
4. & \ 4x^2 - 7x - 2 \\
5. & \ 6x^2 + 16x + 8 \\
6. & \ 4x^2 - 12x + 5 \\
7. & \ x^2 - 8x + 15 \\
8. & \ 3x^2 + 7x + 2 \\
9. & \ 5n^2 + 27n + 10 \\
10. & \ 4x^2 + 14x - 8
\end{aligned}
}
$$