Math worksheet for practicing binomial multiplication using the FOIL method.

It looks like you've uploaded a worksheet titled "Binomial Multiplication (FOIL)", which contains multiple binomial multiplication problems. The goal is to use the FOIL method (First, Outer, Inner, Last) to multiply each pair of binomials.

Let me solve each problem step by step and explain the FOIL method clearly.

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🔷 FOIL Method Explained

FOIL stands for:
- F: First terms
- O: Outer terms
- I: Inner terms
- L: Last terms

For two binomials:
$(a + b)(c + d)$ =
$ac$ (First) + $ad$ (Outer) + $bc$ (Inner) + $bd$ (Last)

Then combine like terms.

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Now let's solve each problem:

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1. $(x - 6)(x + 6)$
F: $x \cdot x = x^2$
O: $x \cdot 6 = 6x$
I: $-6 \cdot x = -6x$
L: $-6 \cdot 6 = -36$
→ $x^2 + 6x - 6x - 36 = x^2 - 36$
✔ Answer: $x^2 - 36$

2. $(y + 7)(y - 8)$
F: $y \cdot y = y^2$
O: $y \cdot (-8) = -8y$
I: $7 \cdot y = 7y$
L: $7 \cdot (-8) = -56$
→ $y^2 - 8y + 7y - 56 = y^2 - y - 56$
✔ Answer: $y^2 - y - 56$

3. $(m + 8)(m - 7)$
F: $m \cdot m = m^2$
O: $m \cdot (-7) = -7m$
I: $8 \cdot m = 8m$
L: $8 \cdot (-7) = -56$
→ $m^2 - 7m + 8m - 56 = m^2 + m - 56$
✔ Answer: $m^2 + m - 56$

4. $(x + 8)(x - 10)$
F: $x \cdot x = x^2$
O: $x \cdot (-10) = -10x$
I: $8 \cdot x = 8x$
L: $8 \cdot (-10) = -80$
→ $x^2 - 10x + 8x - 80 = x^2 - 2x - 80$
✔ Answer: $x^2 - 2x - 80$

5. $(x + 11)(x + 7)$
F: $x \cdot x = x^2$
O: $x \cdot 7 = 7x$
I: $11 \cdot x = 11x$
L: $11 \cdot 7 = 77$
→ $x^2 + 7x + 11x + 77 = x^2 + 18x + 77$
✔ Answer: $x^2 + 18x + 77$

6. $(n - 8)(n + 11)$
F: $n \cdot n = n^2$
O: $n \cdot 11 = 11n$
I: $-8 \cdot n = -8n$
L: $-8 \cdot 11 = -88$
→ $n^2 + 11n - 8n - 88 = n^2 + 3n - 88$
✔ Answer: $n^2 + 3n - 88$

7. $(d + 3)(d + 2)$
F: $d \cdot d = d^2$
O: $d \cdot 2 = 2d$
I: $3 \cdot d = 3d$
L: $3 \cdot 2 = 6$
→ $d^2 + 2d + 3d + 6 = d^2 + 5d + 6$
✔ Answer: $d^2 + 5d + 6$

8. $(h + 8)(h + 7)$
F: $h \cdot h = h^2$
O: $h \cdot 7 = 7h$
I: $8 \cdot h = 8h$
L: $8 \cdot 7 = 56$
→ $h^2 + 7h + 8h + 56 = h^2 + 15h + 56$
✔ Answer: $h^2 + 15h + 56$

9. $(x - 6)(x - 3)$
F: $x \cdot x = x^2$
O: $x \cdot (-3) = -3x$
I: $-6 \cdot x = -6x$
L: $-6 \cdot (-3) = 18$
→ $x^2 - 3x - 6x + 18 = x^2 - 9x + 18$
✔ Answer: $x^2 - 9x + 18$

10. $(x + 5)(x + 6)$
F: $x \cdot x = x^2$
O: $x \cdot 6 = 6x$
I: $5 \cdot x = 5x$
L: $5 \cdot 6 = 30$
→ $x^2 + 6x + 5x + 30 = x^2 + 11x + 30$
✔ Answer: $x^2 + 11x + 30$

11. $(y + 1)(y - 4)$
F: $y \cdot y = y^2$
O: $y \cdot (-4) = -4y$
I: $1 \cdot y = y$
L: $1 \cdot (-4) = -4$
→ $y^2 - 4y + y - 4 = y^2 - 3y - 4$
✔ Answer: $y^2 - 3y - 4$

12. $(m - 2)(m + 5)$
F: $m \cdot m = m^2$
O: $m \cdot 5 = 5m$
I: $-2 \cdot m = -2m$
L: $-2 \cdot 5 = -10$
→ $m^2 + 5m - 2m - 10 = m^2 + 3m - 10$
✔ Answer: $m^2 + 3m - 10$

13. $(x - 10)(x + 6)$
F: $x \cdot x = x^2$
O: $x \cdot 6 = 6x$
I: $-10 \cdot x = -10x$
L: $-10 \cdot 6 = -60$
→ $x^2 + 6x - 10x - 60 = x^2 - 4x - 60$
✔ Answer: $x^2 - 4x - 60$

14. $(x - 7)(x + 6)$
F: $x \cdot x = x^2$
O: $x \cdot 6 = 6x$
I: $-7 \cdot x = -7x$
L: $-7 \cdot 6 = -42$
→ $x^2 + 6x - 7x - 42 = x^2 - x - 42$
✔ Answer: $x^2 - x - 42$

15. $(x - 5)(x - 2)$
F: $x \cdot x = x^2$
O: $x \cdot (-2) = -2x$
I: $-5 \cdot x = -5x$
L: $-5 \cdot (-2) = 10$
→ $x^2 - 2x - 5x + 10 = x^2 - 7x + 10$
✔ Answer: $x^2 - 7x + 10$

16. $(m - 3)(m + 6)$
F: $m \cdot m = m^2$
O: $m \cdot 6 = 6m$
I: $-3 \cdot m = -3m$
L: $-3 \cdot 6 = -18$
→ $m^2 + 6m - 3m - 18 = m^2 + 3m - 18$
✔ Answer: $m^2 + 3m - 18$

17. $(t + 12)(t - 8)$
F: $t \cdot t = t^2$
O: $t \cdot (-8) = -8t$
I: $12 \cdot t = 12t$
L: $12 \cdot (-8) = -96$
→ $t^2 - 8t + 12t - 96 = t^2 + 4t - 96$
✔ Answer: $t^2 + 4t - 96$

18. $(y - 7)(y - 5)$
F: $y \cdot y = y^2$
O: $y \cdot (-5) = -5y$
I: $-7 \cdot y = -7y$
L: $-7 \cdot (-5) = 35$
→ $y^2 - 5y - 7y + 35 = y^2 - 12y + 35$
✔ Answer: $y^2 - 12y + 35$

19. $(x - 8)(x - 7)$
F: $x \cdot x = x^2$
O: $x \cdot (-7) = -7x$
I: $-8 \cdot x = -8x$
L: $-8 \cdot (-7) = 56$
→ $x^2 - 7x - 8x + 56 = x^2 - 15x + 56$
✔ Answer: $x^2 - 15x + 56$

20. $(k - 7)(k - 3)$
F: $k \cdot k = k^2$
O: $k \cdot (-3) = -3k$
I: $-7 \cdot k = -7k$
L: $-7 \cdot (-3) = 21$
→ $k^2 - 3k - 7k + 21 = k^2 - 10k + 21$
✔ Answer: $k^2 - 10k + 21$

21. $(d + 4)(d + 5)$
F: $d \cdot d = d^2$
O: $d \cdot 5 = 5d$
I: $4 \cdot d = 4d$
L: $4 \cdot 5 = 20$
→ $d^2 + 5d + 4d + 20 = d^2 + 9d + 20$
✔ Answer: $d^2 + 9d + 20$

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $x^2 - 36$ |
| 2 | $y^2 - y - 56$ |
| 3 | $m^2 + m - 56$ |
| 4 | $x^2 - 2x - 80$ |
| 5 | $x^2 + 18x + 77$ |
| 6 | $n^2 + 3n - 88$ |
| 7 | $d^2 + 5d + 6$ |
| 8 | $h^2 + 15h + 56$ |
| 9 | $x^2 - 9x + 18$ |
| 10 | $x^2 + 11x + 30$ |
| 11 | $y^2 - 3y - 4$ |
| 12 | $m^2 + 3m - 10$ |
| 13 | $x^2 - 4x - 60$ |
| 14 | $x^2 - x - 42$ |
| 15 | $x^2 - 7x + 10$ |
| 16 | $m^2 + 3m - 18$ |
| 17 | $t^2 + 4t - 96$ |
| 18 | $y^2 - 12y + 35$ |
| 19 | $x^2 - 15x + 56$ |
| 20 | $k^2 - 10k + 21$ |
| 21 | $d^2 + 9d + 20$ |

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