Multiplying Binomials Using The FOIL Method: - Free Printable

To solve the given binomials using the FOIL method, we will follow these steps:

FOIL Method Recap:

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

We will apply this method to each of the given expressions.

---

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

- F: \(x \cdot 2x = 2x^2\)
- O: \(x \cdot 5 = 5x\)
- I: \(2 \cdot 2x = 4x\)
- L: \(2 \cdot 5 = 10\)

Combine all terms:
\[
2x^2 + 5x + 4x + 10 = 2x^2 + 9x + 10
\]

Answer: \(\boxed{2x^2 + 9x + 10}\)

---

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

- F: \(3x \cdot x = 3x^2\)
- O: \(3x \cdot 3 = 9x\)
- I: \(-3 \cdot x = -3x\)
- L: \(-3 \cdot 3 = -9\)

Combine all terms:
\[
3x^2 + 9x - 3x - 9 = 3x^2 + 6x - 9
\]

Answer: \(\boxed{3x^2 + 6x - 9}\)

---

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

- F: \(4a \cdot a = 4a^2\)
- O: \(4a \cdot 3 = 12a\)
- I: \(-5 \cdot a = -5a\)
- L: \(-5 \cdot 3 = -15\)

Combine all terms:
\[
4a^2 + 12a - 5a - 15 = 4a^2 + 7a - 15
\]

Answer: \(\boxed{4a^2 + 7a - 15}\)

---

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

- F: \(2a \cdot a = 2a^2\)
- O: \(2a \cdot 3 = 6a\)
- I: \(1 \cdot a = a\)
- L: \(1 \cdot 3 = 3\)

Combine all terms:
\[
2a^2 + 6a + a + 3 = 2a^2 + 7a + 3
\]

Answer: \(\boxed{2a^2 + 7a + 3}\)

---

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

- F: \(2x \cdot x = 2x^2\)
- O: \(2x \cdot (-8) = -16x\)
- I: \(7 \cdot x = 7x\)
- L: \(7 \cdot (-8) = -56\)

Combine all terms:
\[
2x^2 - 16x + 7x - 56 = 2x^2 - 9x - 56
\]

Answer: \(\boxed{2x^2 - 9x - 56}\)

---

6. \((x + 2)^2\)

This is a special case where we are squaring a binomial. We can use the formula \((A + B)^2 = A^2 + 2AB + B^2\).

Here, \(A = x\) and \(B = 2\):
\[
(x + 2)^2 = x^2 + 2(x)(2) + 2^2 = x^2 + 4x + 4
\]

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

---

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

- F: \(3x \cdot 2x = 6x^2\)
- O: \(3x \cdot 6 = 18x\)
- I: \(1 \cdot 2x = 2x\)
- L: \(1 \cdot 6 = 6\)

Combine all terms:
\[
6x^2 + 18x + 2x + 6 = 6x^2 + 20x + 6
\]

Answer: \(\boxed{6x^2 + 20x + 6}\)

---

8. \((a - 5)^2\)

This is another special case where we are squaring a binomial. We can use the formula \((A - B)^2 = A^2 - 2AB + B^2\).

Here, \(A = a\) and \(B = 5\):
\[
(a - 5)^2 = a^2 - 2(a)(5) + 5^2 = a^2 - 10a + 25
\]

Answer: \(\boxed{a^2 - 10a + 25}\)

---

Final Answers:

1. \((x + 2)(2x + 5) = \boxed{2x^2 + 9x + 10}\)
2. \((3x - 3)(x + 3) = \boxed{3x^2 + 6x - 9}\)
3. \((4a - 5)(a + 3) = \boxed{4a^2 + 7a - 15}\)
4. \((2a + 1)(a + 3) = \boxed{2a^2 + 7a + 3}\)
5. \((2x + 7)(x - 8) = \boxed{2x^2 - 9x - 56}\)
6. \((x + 2)^2 = \boxed{x^2 + 4x + 4}\)
7. \((3x + 1)(2x + 6) = \boxed{6x^2 + 20x + 6}\)
8. \((a - 5)^2 = \boxed{a^2 - 10a + 25}\)