Multiplying Binomials (FOIL) BINGO Game - Free Printable

The image you provided contains a set of problems involving the multiplication of binomials, which is a fundamental concept in algebra. The task is to solve each problem by multiplying the binomials and simplifying the resulting expressions. Below, I will solve each problem step by step and explain the process.

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General Approach:

To multiply two binomials, we use the distributive property (also known as the FOIL method for binomials):
1. First terms
2. Outside terms
3. Inside terms
4. Last terms

After applying the distributive property, combine like terms to simplify the expression.

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Solutions:

#### Problem 1: \( (x + 3)(x - 2) \)
\[
(x + 3)(x - 2) = x \cdot x + x \cdot (-2) + 3 \cdot x + 3 \cdot (-2)
\]
\[
= x^2 - 2x + 3x - 6
\]
\[
= x^2 + x - 6
\]

#### Problem 2: \( (x + 5)(x - 6) \)
\[
(x + 5)(x - 6) = x \cdot x + x \cdot (-6) + 5 \cdot x + 5 \cdot (-6)
\]
\[
= x^2 - 6x + 5x - 30
\]
\[
= x^2 - x - 30
\]

#### Problem 3: \( (x + 7)(x - 8) \)
\[
(x + 7)(x - 8) = x \cdot x + x \cdot (-8) + 7 \cdot x + 7 \cdot (-8)
\]
\[
= x^2 - 8x + 7x - 56
\]
\[
= x^2 - x - 56
\]

#### Problem 4: \( (2x + 3)(x + 5) \)
\[
(2x + 3)(x + 5) = 2x \cdot x + 2x \cdot 5 + 3 \cdot x + 3 \cdot 5
\]
\[
= 2x^2 + 10x + 3x + 15
\]
\[
= 2x^2 + 13x + 15
\]

#### Problem 5: \( (x - 8)(x + 9) \)
\[
(x - 8)(x + 9) = x \cdot x + x \cdot 9 + (-8) \cdot x + (-8) \cdot 9
\]
\[
= x^2 + 9x - 8x - 72
\]
\[
= x^2 + x - 72
\]

#### Problem 6: \( (6x + 2)(x - 3) \)
\[
(6x + 2)(x - 3) = 6x \cdot x + 6x \cdot (-3) + 2 \cdot x + 2 \cdot (-3)
\]
\[
= 6x^2 - 18x + 2x - 6
\]
\[
= 6x^2 - 16x - 6
\]

#### Problem 7: \( (x + 15)(x - 11) \)
\[
(x + 15)(x - 11) = x \cdot x + x \cdot (-11) + 15 \cdot x + 15 \cdot (-11)
\]
\[
= x^2 - 11x + 15x - 165
\]
\[
= x^2 + 4x - 165
\]

#### Problem 8: \( (x + 2)(x - 7) \)
\[
(x + 2)(x - 7) = x \cdot x + x \cdot (-7) + 2 \cdot x + 2 \cdot (-7)
\]
\[
= x^2 - 7x + 2x - 14
\]
\[
= x^2 - 5x - 14
\]

#### Problem 9: \( (x + 1)(x - 8) \)
\[
(x + 1)(x - 8) = x \cdot x + x \cdot (-8) + 1 \cdot x + 1 \cdot (-8)
\]
\[
= x^2 - 8x + x - 8
\]
\[
= x^2 - 7x - 8
\]

#### Problem 10: \( (3x + 1)(x + 4) \)
\[
(3x + 1)(x + 4) = 3x \cdot x + 3x \cdot 4 + 1 \cdot x + 1 \cdot 4
\]
\[
= 3x^2 + 12x + x + 4
\]
\[
= 3x^2 + 13x + 4
\]

#### Problem 11: \( (3x + 7)(x + 8) \)
\[
(3x + 7)(x + 8) = 3x \cdot x + 3x \cdot 8 + 7 \cdot x + 7 \cdot 8
\]
\[
= 3x^2 + 24x + 7x + 56
\]
\[
= 3x^2 + 31x + 56
\]

#### Problem 12: \( (x + 4)(x + 5) \)
\[
(x + 4)(x + 5) = x \cdot x + x \cdot 5 + 4 \cdot x + 4 \cdot 5
\]
\[
= x^2 + 5x + 4x + 20
\]
\[
= x^2 + 9x + 20
\]

#### Problem 13: \( (x + 11)(x + 10) \)
\[
(x + 11)(x + 10) = x \cdot x + x \cdot 10 + 11 \cdot x + 11 \cdot 10
\]
\[
= x^2 + 10x + 11x + 110
\]
\[
= x^2 + 21x + 110
\]

#### Problem 14: \( (x + 1)(x + 7) \)
\[
(x + 1)(x + 7) = x \cdot x + x \cdot 7 + 1 \cdot x + 1 \cdot 7
\]
\[
= x^2 + 7x + x + 7
\]
\[
= x^2 + 8x + 7
\]

#### Problem 15: \( (x + 12)(x + 4) \)
\[
(x + 12)(x + 4) = x \cdot x + x \cdot 4 + 12 \cdot x + 12 \cdot 4
\]
\[
= x^2 + 4x + 12x + 48
\]
\[
= x^2 + 16x + 48
\]

#### Problem 16: \( (x + 13)(x + 7) \)
\[
(x + 13)(x + 7) = x \cdot x + x \cdot 7 + 13 \cdot x + 13 \cdot 7
\]
\[
= x^2 + 7x + 13x + 91
\]
\[
= x^2 + 20x + 91
\]

#### Problem 17: \( (x + 5)(x + 15) \)
\[
(x + 5)(x + 15) = x \cdot x + x \cdot 15 + 5 \cdot x + 5 \cdot 15
\]
\[
= x^2 + 15x + 5x + 75
\]
\[
= x^2 + 20x + 75
\]

#### Problem 18: \( (2x + 5)(x + 9) \)
\[
(2x + 5)(x + 9) = 2x \cdot x + 2x \cdot 9 + 5 \cdot x + 5 \cdot 9
\]
\[
= 2x^2 + 18x + 5x + 45
\]
\[
= 2x^2 + 23x + 45
\]

#### Problem 19: \( (x + 11)(x - 13) \)
\[
(x + 11)(x - 13) = x \cdot x + x \cdot (-13) + 11 \cdot x + 11 \cdot (-13)
\]
\[
= x^2 - 13x + 11x - 143
\]
\[
= x^2 - 2x - 143
\]

#### Problem 20: \( (2x + 3)(x + 9) \)
\[
(2x + 3)(x + 9) = 2x \cdot x + 2x \cdot 9 + 3 \cdot x + 3 \cdot 9
\]
\[
= 2x^2 + 18x + 3x + 27
\]
\[
= 2x^2 + 21x + 27
\]

#### Problem 21: \( (x + 3)^2 \)
\[
(x + 3)^2 = (x + 3)(x + 3)
\]
\[
= x \cdot x + x \cdot 3 + 3 \cdot x + 3 \cdot 3
\]
\[
= x^2 + 3x + 3x + 9
\]
\[
= x^2 + 6x + 9
\]

#### Problem 22: \( (2x + 3)(x + 13) \)
\[
(2x + 3)(x + 13) = 2x \cdot x + 2x \cdot 13 + 3 \cdot x + 3 \cdot 13
\]
\[
= 2x^2 + 26x + 3x + 39
\]
\[
= 2x^2 + 29x + 39
\]

#### Problem 23: \( (x - 8)(x + 9) \)
\[
(x - 8)(x + 9) = x \cdot x + x \cdot 9 + (-8) \cdot x + (-8) \cdot 9
\]
\[
= x^2 + 9x - 8x - 72
\]
\[
= x^2 + x - 72
\]

#### Problem 24: \( (x - 5)(x - 8) \)
\[
(x - 5)(x - 8) = x \cdot x + x \cdot (-8) + (-5) \cdot x + (-5) \cdot (-8)
\]
\[
= x^2 - 8x - 5x + 40
\]
\[
= x^2 - 13x + 40
\]

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Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad x^2 + x - 6 \\
2. & \quad x^2 - x - 30 \\
3. & \quad x^2 - x - 56 \\
4. & \quad 2x^2 + 13x + 15 \\
5. & \quad x^2 + x - 72 \\
6. & \quad 6x^2 - 16x - 6 \\
7. & \quad x^2 + 4x - 165 \\
8. & \quad x^2 - 5x - 14 \\
9. & \quad x^2 - 7x - 8 \\
10. & \quad 3x^2 + 13x + 4 \\
11. & \quad 3x^2 + 31x + 56 \\
12. & \quad x^2 + 9x + 20 \\
13. & \quad x^2 + 21x + 110 \\
14. & \quad x^2 + 8x + 7 \\
15. & \quad x^2 + 16x + 48 \\
16. & \quad x^2 + 20x + 91 \\
17. & \quad x^2 + 20x + 75 \\
18. & \quad 2x^2 + 23x + 45 \\
19. & \quad x^2 - 2x - 143 \\
20. & \quad 2x^2 + 21x + 27 \\
21. & \quad x^2 + 6x + 9 \\
22. & \quad 2x^2 + 29x + 39 \\
23. & \quad x^2 + x - 72 \\
24. & \quad x^2 - 13x + 40 \\
\end{aligned}
}
\]