Algebra worksheet demonstrating the FOIL method with an example and 18 practice problems.

Let's solve each of these problems using the FOIL method, which stands for:

- First
- Outside
- Inside
- Last

This method helps multiply two binomials.

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🔷 Example Recap:

Given: $(x+2)(x+3)$

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

Add them:
$x^2 + 3x + 2x + 6 = x^2 + 5x + 6$

Now let’s apply this to all problems.

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✔ Problem Solutions:

#### ① $(x+3)(x+4)$
- F: $x \cdot x = x^2$
- O: $x \cdot 4 = 4x$
- I: $3 \cdot x = 3x$
- L: $3 \cdot 4 = 12$

Add: $x^2 + 4x + 3x + 12 = x^2 + 7x + 12$

✔ Answer: $x^2 + 7x + 12$

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#### ② $(x+5)(x+2)$
- F: $x^2$
- O: $2x$
- I: $5x$
- L: $10$

Add: $x^2 + 2x + 5x + 10 = x^2 + 7x + 10$

✔ Answer: $x^2 + 7x + 10$

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#### ③ $(x+7)(x+6)$
- F: $x^2$
- O: $6x$
- I: $7x$
- L: $42$

Add: $x^2 + 6x + 7x + 42 = x^2 + 13x + 42$

✔ Answer: $x^2 + 13x + 42$

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#### ④ $(x+5)(x+6)$
- F: $x^2$
- O: $6x$
- I: $5x$
- L: $30$

Add: $x^2 + 6x + 5x + 30 = x^2 + 11x + 30$

✔ Answer: $x^2 + 11x + 30$

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#### ⑤ $(x+8)(x+4)$
- F: $x^2$
- O: $4x$
- I: $8x$
- L: $32$

Add: $x^2 + 4x + 8x + 32 = x^2 + 12x + 32$

✔ Answer: $x^2 + 12x + 32$

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#### ⑥ $(x+10)(x+3)$
- F: $x^2$
- O: $3x$
- I: $10x$
- L: $30$

Add: $x^2 + 3x + 10x + 30 = x^2 + 13x + 30$

✔ Answer: $x^2 + 13x + 30$

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#### ⑦ $(x+9)(x+6)$
- F: $x^2$
- O: $6x$
- I: $9x$
- L: $54$

Add: $x^2 + 6x + 9x + 54 = x^2 + 15x + 54$

✔ Answer: $x^2 + 15x + 54$

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#### ⑧ $(x+4)(x+5)$
- F: $x^2$
- O: $5x$
- I: $4x$
- L: $20$

Add: $x^2 + 5x + 4x + 20 = x^2 + 9x + 20$

✔ Answer: $x^2 + 9x + 20$

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#### ⑨ $(x+6)(x+8)$
- F: $x^2$
- O: $8x$
- I: $6x$
- L: $48$

Add: $x^2 + 8x + 6x + 48 = x^2 + 14x + 48$

✔ Answer: $x^2 + 14x + 48$

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#### ⑩ $(x+10)(x+7)$
- F: $x^2$
- O: $7x$
- I: $10x$
- L: $70$

Add: $x^2 + 7x + 10x + 70 = x^2 + 17x + 70$

✔ Answer: $x^2 + 17x + 70$

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#### ⑪ $(x+3)(x+9)$
- F: $x^2$
- O: $9x$
- I: $3x$
- L: $27$

Add: $x^2 + 9x + 3x + 27 = x^2 + 12x + 27$

✔ Answer: $x^2 + 12x + 27$

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#### ⑫ $(x+12)(x+3)$
- F: $x^2$
- O: $3x$
- I: $12x$
- L: $36$

Add: $x^2 + 3x + 12x + 36 = x^2 + 15x + 36$

✔ Answer: $x^2 + 15x + 36$

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#### ⑬ $(x+7)(x+6)$
Same as #3 → $x^2 + 13x + 42$

✔ Answer: $x^2 + 13x + 42$

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#### ⑭ $(x+5)(x+5)$
This is a perfect square: $(x+5)^2$

- F: $x^2$
- O: $5x$
- I: $5x$
- L: $25$

Add: $x^2 + 5x + 5x + 25 = x^2 + 10x + 25$

✔ Answer: $x^2 + 10x + 25$

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#### ⑮ $(x+3)(x+8)$
- F: $x^2$
- O: $8x$
- I: $3x$
- L: $24$

Add: $x^2 + 8x + 3x + 24 = x^2 + 11x + 24$

✔ Answer: $x^2 + 11x + 24$

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#### ⑯ $(x+15)(x+3)$
- F: $x^2$
- O: $3x$
- I: $15x$
- L: $45$

Add: $x^2 + 3x + 15x + 45 = x^2 + 18x + 45$

✔ Answer: $x^2 + 18x + 45$

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#### ⑰ $(2x+3)(x+2)$
Now we have coefficients on $x$, so be careful!

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

Add: $2x^2 + 4x + 3x + 6 = 2x^2 + 7x + 6$

✔ Answer: $2x^2 + 7x + 6$

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#### ⑱ $(3x+1)(2x+5)$
- F: $3x \cdot 2x = 6x^2$
- O: $3x \cdot 5 = 15x$
- I: $1 \cdot 2x = 2x$
- L: $1 \cdot 5 = 5$

Add: $6x^2 + 15x + 2x + 5 = 6x^2 + 17x + 5$

✔ Answer: $6x^2 + 17x + 5$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| ① | $x^2 + 7x + 12$ |
| ② | $x^2 + 7x + 10$ |
| ③ | $x^2 + 13x + 42$ |
| ④ | $x^2 + 11x + 30$ |
| ⑤ | $x^2 + 12x + 32$ |
| ⑥ | $x^2 + 13x + 30$ |
| ⑦ | $x^2 + 15x + 54$ |
| ⑧ | $x^2 + 9x + 20$ |
| ⑨ | $x^2 + 14x + 48$ |
| ⑩ | $x^2 + 17x + 70$ |
| ⑪ | $x^2 + 12x + 27$ |
| ⑫ | $x^2 + 15x + 36$ |
| ⑬ | $x^2 + 13x + 42$ |
| ⑭ | $x^2 + 10x + 25$ |
| ⑮ | $x^2 + 11x + 24$ |
| ⑯ | $x^2 + 18x + 45$ |
| ⑰ | $2x^2 + 7x + 6$ |
| ⑱ | $6x^2 + 17x + 5$ |

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📝 Summary:

The FOIL method is a reliable way to expand binomials. Always:
1. Multiply First terms
2. Multiply Outside terms
3. Multiply Inside terms
4. Multiply Last terms
5. Combine like terms (especially the middle terms)

Let me know if you want these written out step-by-step or formatted neatly!