SOLUTION: Foil worksheet multiplying binomials - Studypool - Free Printable

Problem: Multiplying Binomials Using the FOIL Method

The task is to find the product of each pair of 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 step by step to each problem.

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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: \(\boxed{x^2 + 2x + 1}\)

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#### 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: \(\boxed{x^2 + 3x + 2}\)

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#### 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: \(\boxed{x^2 + 5x + 6}\)

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#### 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: \(\boxed{x^2 + 5x + 6}\)

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#### 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: \(\boxed{x^2 + 7x + 12}\)

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#### 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: \(\boxed{x^2 - 9x + 20}\)

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#### 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: \(\boxed{3y^2 + 20y + 12}\)

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#### 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: \(\boxed{4x^2 + 4x + 1}\)

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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. \(\boxed{4x^2 + 4x + 1}\)