Worksheet for practicing the multiplication of binomials using the FOIL method, featuring 11 algebraic problems and a visual guide.

Problem Overview:

The task involves multiplying binomials using the FOIL method. The FOIL method is an acronym that stands for:

- F: First terms
- O: Outer terms
- I: Inner terms
- L: Last terms

We will apply this method to each of the given problems step by step.

---

Solution:

#### 1. (x + 1)(x + 1)

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

Combine all terms:
\[
x^2 + x + x + 1 = x^2 + 2x + 1
\]

Answer:
\[
\boxed{x^2 + 2x + 1}
\]

---

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

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

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

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

---

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

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

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

Answer:
\[
\boxed{x^2 + 5x + 6}
\]

---

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

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

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

Answer:
\[
\boxed{x^2 + 5x + 6}
\]

---

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

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

Combine all terms:
\[
x^2 + 3x + 4x + 12 = x^2 + 7x + 12
\]

Answer:
\[
\boxed{x^2 + 7x + 12}
\]

---

#### 6. (x - 6)(x + 2)

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

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

Answer:
\[
\boxed{x^2 - 4x - 12}
\]

---

#### 7. (x - 5)(x - 4)

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

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

Answer:
\[
\boxed{x^2 - 9x + 20}
\]

---

#### 8. (y + 6)(y + 5)

Using FOIL:
- F: \( y \cdot y = y^2 \)
- O: \( y \cdot 5 = 5y \)
- I: \( 6 \cdot y = 6y \)
- L: \( 6 \cdot 5 = 30 \)

Combine all terms:
\[
y^2 + 5y + 6y + 30 = y^2 + 11y + 30
\]

Answer:
\[
\boxed{y^2 + 11y + 30}
\]

---

#### 9. (2x + 1)(x + 2)

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

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

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

---

#### 10. (y + 6)(3y + 2)

Using FOIL:
- F: \( y \cdot 3y = 3y^2 \)
- O: \( y \cdot 2 = 2y \)
- I: \( 6 \cdot 3y = 18y \)
- L: \( 6 \cdot 2 = 12 \)

Combine all terms:
\[
3y^2 + 2y + 18y + 12 = 3y^2 + 20y + 12
\]

Answer:
\[
\boxed{3y^2 + 20y + 12}
\]

---

#### 11. (2x + 1)(2x + 1)

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

Combine all terms:
\[
4x^2 + 2x + 2x + 1 = 4x^2 + 4x + 1
\]

Answer:
\[
\boxed{4x^2 + 4x + 1}
\]

---

Final Answers:

1. \(\boxed{x^2 + 2x + 1}\)
2. \(\boxed{x^2 + 3x + 2}\)
3. \(\boxed{x^2 + 5x + 6}\)
4. \(\boxed{x^2 + 5x + 6}\)
5. \(\boxed{x^2 + 7x + 12}\)
6. \(\boxed{x^2 - 4x - 12}\)
7. \(\boxed{x^2 - 9x + 20}\)
8. \(\boxed{y^2 + 11y + 30}\)
9. \(\boxed{2x^2 + 5x + 2}\)
10. \(\boxed{3y^2 + 20y + 12}\)
11. \(\boxed{4x^2 + 4x + 1}\)