Multiplying Monomials FOIL Method - Free Printable

You’ve uploaded a worksheet titled “Multiplying Binomials”, and it appears you want me to verify the solutions or explain how to solve each problem. The red answers are already filled in — I’ll go through each one, show the correct steps using the FOIL method (First, Outer, Inner, Last), and confirm whether the given answer is correct.

---

## ✔ General Method: FOIL
For multiplying two binomials `(a + b)(c + d)`:
- First: `a * c`
- Outer: `a * d`
- Inner: `b * c`
- Last: `b * d`
Then combine like terms.

---

1. `(2x + y)(x - 2y)`

- F: `2x * x = 2x²`
- O: `2x * (-2y) = -4xy`
- I: `y * x = xy`
- L: `y * (-2y) = -2y²`
→ Combine: `2x² - 4xy + xy - 2y² = 2x² - 3xy - 2y²` ✔
Given answer: Correct

---

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

- F: `x * 2x = 2x²`
- O: `x * (-y) = -xy`
- I: `-3y * 2x = -6xy`
- L: `-3y * (-y) = 3y²`
→ Combine: `2x² - xy - 6xy + 3y² = 2x² - 7xy + 3y²` ✔
Given answer: Correct

---

3. `(x - 4)(2x - 1)`

- F: `x * 2x = 2x²`
- O: `x * (-1) = -x`
- I: `-4 * 2x = -8x`
- L: `-4 * (-1) = 4`
→ Combine: `2x² - x - 8x + 4 = 2x² - 9x + 4` ✔
Given answer: Correct

---

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

- F: `x * 2x = 2x²`
- O: `x * 3 = 3x`
- I: `2 * 2x = 4x`
- L: `2 * 3 = 6`
→ Combine: `2x² + 3x + 4x + 6 = 2x² + 7x + 6` ✔
Given answer: Correct

---

5. `(2x + 4)(x - 3)`

- F: `2x * x = 2x²`
- O: `2x * (-3) = -6x`
- I: `4 * x = 4x`
- L: `4 * (-3) = -12`
→ Combine: `2x² - 6x + 4x - 12 = 2x² - 2x - 12` ✔
Given answer: Correct

---

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

- F: `2x * x = 2x²`
- O: `2x * 2 = 4x`
- I: `1 * x = x`
- L: `1 * 2 = 2`
→ Combine: `2x² + 4x + x + 2 = 2x² + 5x + 2` ✔
Given answer: Correct

---

7. `(3x - 3y)(2x - y)`

- F: `3x * 2x = 6x²`
- O: `3x * (-y) = -3xy`
- I: `-3y * 2x = -6xy`
- L: `-3y * (-y) = 3y²`
→ Combine: `6x² - 3xy - 6xy + 3y² = 6x² - 9xy + 3y²` ✔
Given answer: Correct

---

8. `(x - 3)(2x - 1)`

- F: `x * 2x = 2x²`
- O: `x * (-1) = -x`
- I: `-3 * 2x = -6x`
- L: `-3 * (-1) = 3`
→ Combine: `2x² - x - 6x + 3 = 2x² - 7x + 3`

⚠️ BUT THE GIVEN ANSWER IS `6x² - 9xy + 3y²` — THIS IS WRONG!

This looks like a copy-paste error — they reused the answer from problem #7. This problem has no `y` variables!

✔ Correct Answer: `2x² - 7x + 3`

---

9. `(x + 2y)(2x - y)`

- F: `x * 2x = 2x²`
- O: `x * (-y) = -xy`
- I: `2y * 2x = 4xy`
- L: `2y * (-y) = -2y²`
→ Combine: `2x² - xy + 4xy - 2y² = 2x² + 3xy - 2y²` ✔
Given answer: Correct

---

10. `(2x + 1)(x + 2)`

- F: `2x * x = 2x²`
- O: `2x * 2 = 4x`
- I: `1 * x = x`
- L: `1 * 2 = 2`
→ Combine: `2x² + 4x + x + 2 = 2x² + 5x + 2` ✔
Given answer: Correct

---

## 📝 Summary of Corrections:

| Problem | Given Answer | Correct Answer | Status |
|---------|--------------|----------------|--------|
| 1 | 2x² - 3xy - 2y² | Same | ✔ Correct |
| 2 | 2x² - 7xy + 3y² | Same | ✔ Correct |
| 3 | 2x² - 9x + 4 | Same | ✔ Correct |
| 4 | 2x² + 7x + 6 | Same | ✔ Correct |
| 5 | 2x² - 2x - 12 | Same | ✔ Correct |
| 6 | 2x² + 5x + 2 | Same | ✔ Correct |
| 7 | 6x² - 9xy + 3y² | Same | ✔ Correct |
| 8 | 6x² - 9xy + 3y² | 2x² - 7x + 3 | ✘ Incorrect — typo! |
| 9 | 2x² + 3xy - 2y² | Same | ✔ Correct |
| 10 | 2x² + 5x + 2 | Same | ✔ Correct |

---

## 💡 Final Note:
Problem #8 is the only one with an incorrect answer. It likely happened because the student copied the answer from problem #7 by mistake. Always double-check variable types — if there’s no `y` in the original problem, your answer shouldn’t have `y` either!

Let me know if you’d like a printable version or step-by-step video-style walkthroughs for any of these!