Multiplying Binomials Using The FOIL Method: - Free Printable

Absolutely! Let’s solve each of these binomial multiplication problems using the FOIL method.

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📌 What is FOIL?

FOIL stands for:
- First → Multiply the first terms in each binomial
- Outer → Multiply the outer terms
- Inner → Multiply the inner terms
- Last → Multiply the last terms

Then, combine like terms to simplify.

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Let’s go one by one:

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1. `(x + 2)(2x + 5)`

- F: `x * 2x = 2x²`
- O: `x * 5 = 5x`
- I: `2 * 2x = 4x`
- L: `2 * 5 = 10`

→ Combine: `2x² + 5x + 4x + 10 = 2x² + 9x + 10`

✔ Answer: `2x² + 9x + 10`

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2. `(3x - 3)(x + 3)`

- F: `3x * x = 3x²`
- O: `3x * 3 = 9x`
- I: `-3 * x = -3x`
- L: `-3 * 3 = -9`

→ Combine: `3x² + 9x - 3x - 9 = 3x² + 6x - 9`

✔ Answer: `3x² + 6x - 9`

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3. `(4a - 5)(a + 3)`

- F: `4a * a = 4a²`
- O: `4a * 3 = 12a`
- I: `-5 * a = -5a`
- L: `-5 * 3 = -15`

→ Combine: `4a² + 12a - 5a - 15 = 4a² + 7a - 15`

✔ Answer: `4a² + 7a - 15`

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4. `(2a + 1)(a + 3)`

- F: `2a * a = 2a²`
- O: `2a * 3 = 6a`
- I: `1 * a = a`
- L: `1 * 3 = 3`

→ Combine: `2a² + 6a + a + 3 = 2a² + 7a + 3`

✔ Answer: `2a² + 7a + 3`

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5. `(2x + 7)(x - 8)`

- F: `2x * x = 2x²`
- O: `2x * (-8) = -16x`
- I: `7 * x = 7x`
- L: `7 * (-8) = -56`

→ Combine: `2x² - 16x + 7x - 56 = 2x² - 9x - 56`

✔ Answer: `2x² - 9x - 56`

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6. `(x + 2)²`

This is the same as `(x + 2)(x + 2)` — so we apply FOIL.

- F: `x * x = x²`
- O: `x * 2 = 2x`
- I: `2 * x = 2x`
- L: `2 * 2 = 4`

→ Combine: `x² + 2x + 2x + 4 = x² + 4x + 4`

✔ Answer: `x² + 4x + 4`

*(Note: This is also a perfect square trinomial: `(a + b)² = a² + 2ab + b²`)*

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7. `(3x + 1)(2x + 6)`

- F: `3x * 2x = 6x²`
- O: `3x * 6 = 18x`
- I: `1 * 2x = 2x`
- L: `1 * 6 = 6`

→ Combine: `6x² + 18x + 2x + 6 = 6x² + 20x + 6`

✔ Answer: `6x² + 20x + 6`

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8. `(a - 5)²`

Same as `(a - 5)(a - 5)`

- F: `a * a = a²`
- O: `a * (-5) = -5a`
- I: `-5 * a = -5a`
- L: `-5 * (-5) = 25`

→ Combine: `a² - 5a - 5a + 25 = a² - 10a + 25`

✔ Answer: `a² - 10a + 25`

*(Perfect square trinomial: `(a - b)² = a² - 2ab + b²`)*

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## ✔ Final Answers Summary:

1. `(x + 2)(2x + 5)` = `2x² + 9x + 10`
2. `(3x - 3)(x + 3)` = `3x² + 6x - 9`
3. `(4a - 5)(a + 3)` = `4a² + 7a - 15`
4. `(2a + 1)(a + 3)` = `2a² + 7a + 3`
5. `(2x + 7)(x - 8)` = `2x² - 9x - 56`
6. `(x + 2)²` = `x² + 4x + 4`
7. `(3x + 1)(2x + 6)` = `6x² + 20x + 6`
8. `(a - 5)²` = `a² - 10a + 25`

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Let me know if you’d like to see any of these with step-by-step diagrams or video-style explanations! 😊