Algebra worksheet practicing the FOIL method to multiply binomials.

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.

---

Solution:

#### 1. (4x - 5)(x - 3)

Using FOIL:
- F: \(4x \cdot x = 4x^2\)
- O: \(4x \cdot (-3) = -12x\)
- I: \((-5) \cdot x = -5x\)
- L: \((-5) \cdot (-3) = 15\)

Combine all terms:
\[
4x^2 - 12x - 5x + 15 = 4x^2 - 17x + 15
\]

Answer:
\[
\boxed{4x^2 - 17x + 15}
\]

---

#### 2. (4x - 4)(x - 4)

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

Combine all terms:
\[
4x^2 - 16x - 4x + 16 = 4x^2 - 20x + 16
\]

Answer:
\[
\boxed{4x^2 - 20x + 16}
\]

---

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

Using FOIL:
- F: \(2x \cdot 3x = 6x^2\)
- O: \(2x \cdot 5 = 10x\)
- I: \(2 \cdot 3x = 6x\)
- L: \(2 \cdot 5 = 10\)

Combine all terms:
\[
6x^2 + 10x + 6x + 10 = 6x^2 + 16x + 10
\]

Answer:
\[
\boxed{6x^2 + 16x + 10}
\]

---

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

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

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

Answer:
\[
\boxed{12x^2 + 6x - 6}
\]

---

#### 5. (x - 1)(2x + 5)

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

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

Answer:
\[
\boxed{2x^2 + 3x - 5}
\]

---

#### 6. (5x + 2)(4x + 4)

Using FOIL:
- F: \(5x \cdot 4x = 20x^2\)
- O: \(5x \cdot 4 = 20x\)
- I: \(2 \cdot 4x = 8x\)
- L: \(2 \cdot 4 = 8\)

Combine all terms:
\[
20x^2 + 20x + 8x + 8 = 20x^2 + 28x + 8
\]

Answer:
\[
\boxed{20x^2 + 28x + 8}
\]

---

#### 7. (3x - 3)(x - 2)

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

Combine all terms:
\[
3x^2 - 6x - 3x + 6 = 3x^2 - 9x + 6
\]

Answer:
\[
\boxed{3x^2 - 9x + 6}
\]

---

#### 8. (4x + 1)(3x + 2)

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

Combine all terms:
\[
12x^2 + 8x + 3x + 2 = 12x^2 + 11x + 2
\]

Answer:
\[
\boxed{12x^2 + 11x + 2}
\]

---

#### 9. (5x + 3)(3x + 4)

Using FOIL:
- F: \(5x \cdot 3x = 15x^2\)
- O: \(5x \cdot 4 = 20x\)
- I: \(3 \cdot 3x = 9x\)
- L: \(3 \cdot 4 = 12\)

Combine all terms:
\[
15x^2 + 20x + 9x + 12 = 15x^2 + 29x + 12
\]

Answer:
\[
\boxed{15x^2 + 29x + 12}
\]

---

#### 10. (3x - 3)(3x + 2)

Using FOIL:
- F: \(3x \cdot 3x = 9x^2\)
- O: \(3x \cdot 2 = 6x\)
- I: \((-3) \cdot 3x = -9x\)
- L: \((-3) \cdot 2 = -6\)

Combine all terms:
\[
9x^2 + 6x - 9x - 6 = 9x^2 - 3x - 6
\]

Answer:
\[
\boxed{9x^2 - 3x - 6}
\]

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Final Answers:

1. \(\boxed{4x^2 - 17x + 15}\)
2. \(\boxed{4x^2 - 20x + 16}\)
3. \(\boxed{6x^2 + 16x + 10}\)
4. \(\boxed{12x^2 + 6x - 6}\)
5. \(\boxed{2x^2 + 3x - 5}\)
6. \(\boxed{20x^2 + 28x + 8}\)
7. \(\boxed{3x^2 - 9x + 6}\)
8. \(\boxed{12x^2 + 11x + 2}\)
9. \(\boxed{15x^2 + 29x + 12}\)
10. \(\boxed{9x^2 - 3x - 6}\)