SOLUTION: Foil worksheet multiplying binomials - Studypool - Free Printable

Let's solve each problem on the "Multiplying Binomials FOIL Practice Worksheet" step by step using the FOIL method.

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🔷 What is FOIL?

FOIL stands for:
- First: Multiply the first terms in each binomial.
- Outside: Multiply the outer terms.
- Inside: Multiply the inner terms.
- Last: Multiply the last terms in each binomial.

Then, combine like terms.

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Now let’s go through each problem:

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

- F: $x \cdot x = x^2$
- O: $x \cdot 1 = x$
- I: $1 \cdot x = x$
- L: $1 \cdot 1 = 1$

Add them:
$x^2 + x + x + 1 = x^2 + 2x + 1$

✔ Answer: $x^2 + 2x + 1$

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2. $(x + 1)(x + 2)$

- F: $x \cdot x = x^2$
- O: $x \cdot 2 = 2x$
- I: $1 \cdot x = x$
- L: $1 \cdot 2 = 2$

Add:
$x^2 + 2x + x + 2 = x^2 + 3x + 2$

✔ Answer: $x^2 + 3x + 2$

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

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

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

✔ Answer: $x^2 + 5x + 6$

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

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

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

✔ Answer: $x^2 + 5x + 6$

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

- F: $x \cdot x = x^2$
- O: $x \cdot 3 = 3x$
- I: $4 \cdot x = 4x$
- L: $4 \cdot 3 = 12$

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

✔ Answer: $x^2 + 7x + 12$

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

- F: $x \cdot x = x^2$
- O: $x \cdot 2 = 2x$
- I: $-6 \cdot x = -6x$
- L: $-6 \cdot 2 = -12$

Add:
$x^2 + 2x - 6x - 12 = x^2 - 4x - 12$

✔ Answer: $x^2 - 4x - 12$

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

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

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

✔ Answer: $x^2 - 9x + 20$

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

- F: $y \cdot y = y^2$
- O: $y \cdot 5 = 5y$
- I: $6 \cdot y = 6y$
- L: $6 \cdot 5 = 30$

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

✔ Answer: $y^2 + 11y + 30$

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

- F: $2x \cdot x = 2x^2$
- O: $2x \cdot 2 = 4x$
- I: $1 \cdot x = x$
- L: $1 \cdot 2 = 2$

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

✔ Answer: $2x^2 + 5x + 2$

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

- F: $y \cdot 3y = 3y^2$
- O: $y \cdot 2 = 2y$
- I: $6 \cdot 3y = 18y$
- L: $6 \cdot 2 = 12$

Add:
$3y^2 + 2y + 18y + 12 = 3y^2 + 20y + 12$

✔ Answer: $3y^2 + 20y + 12$

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

This is a perfect square: $(a + b)^2 = a^2 + 2ab + b^2$, but we'll use FOIL.

- F: $2x \cdot 2x = 4x^2$
- O: $2x \cdot 1 = 2x$
- I: $1 \cdot 2x = 2x$
- L: $1 \cdot 1 = 1$

Add:
$4x^2 + 2x + 2x + 1 = 4x^2 + 4x + 1$

✔ Answer: $4x^2 + 4x + 1$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $x^2 + 2x + 1$ |
| 2 | $x^2 + 3x + 2$ |
| 3 | $x^2 + 5x + 6$ |
| 4 | $x^2 + 5x + 6$ |
| 5 | $x^2 + 7x + 12$ |
| 6 | $x^2 - 4x - 12$ |
| 7 | $x^2 - 9x + 20$ |
| 8 | $y^2 + 11y + 30$ |
| 9 | $2x^2 + 5x + 2$ |
| 10 | $3y^2 + 20y + 12$ |
| 11 | $4x^2 + 4x + 1$ |

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