Comprehensive worksheet for practicing the multiplication of binomials using both the box method and the FOIL technique.

Of course! I'll solve each problem on the "Multiplying Binomials FOIL Practice Worksheet" and explain the solution step by step.

The FOIL method stands for:
- First: Multiply the first terms in each binomial.
- Outer: Multiply the outer terms in the product.
- Inner: Multiply the inner terms.
- Last: Multiply the last terms in each binomial.

Then, you combine like terms to get the final answer.

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

- F: x * x = x²
- O: x * 1 = x
- I: 1 * x = x
- L: 1 * 1 = 1

Add them: x² + x + x + 1 = x² + 2x + 1

✔ Answer: x² + 2x + 1

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

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

Add them: x² + 3x + 2x + 6 = x² + 5x + 6

✔ Answer: x² + 5x + 6

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

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

Add them: x² + 2x - 3x - 6 = x² - x - 6

✔ Answer: x² - x - 6

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

- F: x * x = x²
- O: x * 2 = 2x
- I: -6 * x = -6x
- L: -6 * 2 = -12

Add them: x² + 2x - 6x - 12 = x² - 4x - 12

✔ Answer: x² - 4x - 12

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5. (x - 5)(x - 4)

- F: x * x = x²
- O: x * (-4) = -4x
- I: -5 * x = -5x
- L: -5 * (-4) = 20

Add them: x² - 4x - 5x + 20 = x² - 9x + 20

✔ Answer: x² - 9x + 20

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

- F: y * 3y = 3y²
- O: y * 2 = 2y
- I: 6 * 3y = 18y
- L: 6 * 2 = 12

Add them: 3y² + 2y + 18y + 12 = 3y² + 20y + 12

✔ Answer: 3y² + 20y + 12

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7. (2x + 1)(x + 2)

Let’s fill in the FOIL parts as requested:

- F: 2x * x = 2x²
- O: 2x * 2 = 4x
- I: 1 * x = x
- L: 1 * 2 = 2

Now add them: 2x² + 4x + x + 2 = 2x² + 5x + 2

✔ Answer: 2x² + 5x + 2

FOIL breakdown:
- F = 2x²
- O = 4x
- I = x
- L = 2

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8. (2x - 1)(2x + 1)

This is a difference of squares pattern: (a - b)(a + b) = a² - b²

But let’s do it with FOIL:

- F: 2x * 2x = 4x²
- O: 2x * 1 = 2x
- I: -1 * 2x = -2x
- L: -1 * 1 = -1

Add them: 4x² + 2x - 2x - 1 = 4x² - 1

✔ Answer: 4x² - 1

FOIL breakdown:
- F = 4x²
- O = 2x
- I = -2x
- L = -1

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## ✔ Final Answers Summary:

1. x² + 2x + 1
2. x² + 5x + 6
3. x² - x - 6
4. x² - 4x - 12
5. x² - 9x + 20
6. 3y² + 20y + 12
7. 2x² + 5x + 2 → F=2x², O=4x, I=x, L=2
8. 4x² - 1 → F=4x², O=2x, I=-2x, L=-1

Let me know if you’d like to see how to use the area model (the boxes) for any of these!