Math worksheet for practicing multiplying binomials, with 20 problems and a colorful answer key.

It looks like you've uploaded a worksheet titled "Practice: Multiplying Binomials", with 20 problems asking to multiply two binomials and write the result in expanded form:
$$
ax^2 + bx + c
$$

Additionally, there's a small image at the bottom right showing an example:
- $ x = -5 $
- $ 6x^2 - 30x + 12 $
- $ 6(-5)^2 - 30(-5) + 12 = 6(25) + 150 + 12 = 150 + 150 + 12 = 312 $

But this seems to be just an example of evaluating a quadratic expression — not directly related to the main task.

Let’s solve each problem on the worksheet step-by-step using the FOIL method (First, Outer, Inner, Last), which is used to multiply two binomials.

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🔷 Problem 1: $(5x - 2)(2x + 5)$

$$
= 5x \cdot 2x + 5x \cdot 5 - 2 \cdot 2x - 2 \cdot 5 \\
= 10x^2 + 25x - 4x - 10 \\
= 10x^2 + 21x - 10
$$

✔ Answer: $10x^2 + 21x - 10$

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🔷 Problem 2: $(2x - 3)(x + 4)$

$$
= 2x \cdot x + 2x \cdot 4 - 3 \cdot x - 3 \cdot 4 \\
= 2x^2 + 8x - 3x - 12 \\
= 2x^2 + 5x - 12
$$

✔ Answer: $2x^2 + 5x - 12$

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🔷 Problem 3: $(2m + 1)(5m + 5)$

$$
= 2m \cdot 5m + 2m \cdot 5 + 1 \cdot 5m + 1 \cdot 5 \\
= 10m^2 + 10m + 5m + 5 \\
= 10m^2 + 15m + 5
$$

✔ Answer: $10m^2 + 15m + 5$

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🔷 Problem 4: $(3a + 3)(5a - 1)$

$$
= 3a \cdot 5a + 3a \cdot (-1) + 3 \cdot 5a + 3 \cdot (-1) \\
= 15a^2 - 3a + 15a - 3 \\
= 15a^2 + 12a - 3
$$

✔ Answer: $15a^2 + 12a - 3$

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🔷 Problem 5: $(4k + 3)(5k + 1)$

$$
= 4k \cdot 5k + 4k \cdot 1 + 3 \cdot 5k + 3 \cdot 1 \\
= 20k^2 + 4k + 15k + 3 \\
= 20k^2 + 19k + 3
$$

✔ Answer: $20k^2 + 19k + 3$

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🔷 Problem 6: $(3r + 3)(5r + 1)$

$$
= 3r \cdot 5r + 3r \cdot 1 + 3 \cdot 5r + 3 \cdot 1 \\
= 15r^2 + 3r + 15r + 3 \\
= 15r^2 + 18r + 3
$$

✔ Answer: $15r^2 + 18r + 3$

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🔷 Problem 7: $(5x - 4)(5x + 3)$

$$
= 5x \cdot 5x + 5x \cdot 3 - 4 \cdot 5x - 4 \cdot 3 \\
= 25x^2 + 15x - 20x - 12 \\
= 25x^2 - 5x - 12
$$

✔ Answer: $25x^2 - 5x - 12$

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🔷 Problem 8: $(3r + 3)(2r - 1)$

$$
= 3r \cdot 2r + 3r \cdot (-1) + 3 \cdot 2r + 3 \cdot (-1) \\
= 6r^2 - 3r + 6r - 3 \\
= 6r^2 + 3r - 3
$$

✔ Answer: $6r^2 + 3r - 3$

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🔷 Problem 9: $(3m - 3)(3m + 5)$

$$
= 3m \cdot 3m + 3m \cdot 5 - 3 \cdot 3m - 3 \cdot 5 \\
= 9m^2 + 15m - 9m - 15 \\
= 9m^2 + 6m - 15
$$

✔ Answer: $9m^2 + 6m - 15$

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🔷 Problem 10: $(4x + 2)(x - 1)$

$$
= 4x \cdot x + 4x \cdot (-1) + 2 \cdot x + 2 \cdot (-1) \\
= 4x^2 - 4x + 2x - 2 \\
= 4x^2 - 2x - 2
$$

✔ Answer: $4x^2 - 2x - 2$

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🔷 Problem 11: $(-2n - 6)(5n - 3)$

$$
= -2n \cdot 5n + (-2n) \cdot (-3) + (-6) \cdot 5n + (-6) \cdot (-3) \\
= -10n^2 + 6n - 30n + 18 \\
= -10n^2 - 24n + 18
$$

✔ Answer: $-10n^2 - 24n + 18$

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🔷 Problem 12: $(-7h + 7)(-6h - 6)$

$$
= -7h \cdot (-6h) + (-7h) \cdot (-6) + 7 \cdot (-6h) + 7 \cdot (-6) \\
= 42h^2 + 42h - 42h - 42 \\
= 42h^2 - 42
$$

✔ Answer: $42h^2 - 42$

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🔷 Problem 13: $(4b - 8)(-8b - 8)$

$$
= 4b \cdot (-8b) + 4b \cdot (-8) + (-8) \cdot (-8b) + (-8) \cdot (-8) \\
= -32b^2 - 32b + 64b + 64 \\
= -32b^2 + 32b + 64
$$

✔ Answer: $-32b^2 + 32b + 64$

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🔷 Problem 14: $(7a - 2)(-2a + 7)$

$$
= 7a \cdot (-2a) + 7a \cdot 7 + (-2) \cdot (-2a) + (-2) \cdot 7 \\
= -14a^2 + 49a + 4a - 14 \\
= -14a^2 + 53a - 14
$$

✔ Answer: $-14a^2 + 53a - 14$

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🔷 Problem 15: $(2p + 5)(-8p + 5)$

$$
= 2p \cdot (-8p) + 2p \cdot 5 + 5 \cdot (-8p) + 5 \cdot 5 \\
= -16p^2 + 10p - 40p + 25 \\
= -16p^2 - 30p + 25
$$

✔ Answer: $-16p^2 - 30p + 25$

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🔷 Problem 16: $(-a - 2)(-7a + 7)$

$$
= -a \cdot (-7a) + (-a) \cdot 7 + (-2) \cdot (-7a) + (-2) \cdot 7 \\
= 7a^2 - 7a + 14a - 14 \\
= 7a^2 + 7a - 14
$$

✔ Answer: $7a^2 + 7a - 14$

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🔷 Problem 17: $(-8n - 4)(-4n + 3)$

$$
= -8n \cdot (-4n) + (-8n) \cdot 3 + (-4) \cdot (-4n) + (-4) \cdot 3 \\
= 32n^2 - 24n + 16n - 12 \\
= 32n^2 - 8n - 12
$$

✔ Answer: $32n^2 - 8n - 12$

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🔷 Problem 18: $(-4n - 6)(4n - 8)$

$$
= -4n \cdot 4n + (-4n) \cdot (-8) + (-6) \cdot 4n + (-6) \cdot (-8) \\
= -16n^2 + 32n - 24n + 48 \\
= -16n^2 + 8n + 48
$$

✔ Answer: $-16n^2 + 8n + 48$

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🔷 Problem 19: $(5m - 1)(7m + 8)$

$$
= 5m \cdot 7m + 5m \cdot 8 + (-1) \cdot 7m + (-1) \cdot 8 \\
= 35m^2 + 40m - 7m - 8 \\
= 35m^2 + 33m - 8
$$

✔ Answer: $35m^2 + 33m - 8$

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🔷 Problem 20: $(7n - 2)(-n + 8)$

$$
= 7n \cdot (-n) + 7n \cdot 8 + (-2) \cdot (-n) + (-2) \cdot 8 \\
= -7n^2 + 56n + 2n - 16 \\
= -7n^2 + 58n - 16
$$

✔ Answer: $-7n^2 + 58n - 16$

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## ✔ Final Answers Summary:

| # | Answer |
|---|--------|
| 1 | $10x^2 + 21x - 10$ |
| 2 | $2x^2 + 5x - 12$ |
| 3 | $10m^2 + 15m + 5$ |
| 4 | $15a^2 + 12a - 3$ |
| 5 | $20k^2 + 19k + 3$ |
| 6 | $15r^2 + 18r + 3$ |
| 7 | $25x^2 - 5x - 12$ |
| 8 | $6r^2 + 3r - 3$ |
| 9 | $9m^2 + 6m - 15$ |
|10 | $4x^2 - 2x - 2$ |
|11 | $-10n^2 - 24n + 18$ |
|12 | $42h^2 - 42$ |
|13 | $-32b^2 + 32b + 64$ |
|14 | $-14a^2 + 53a - 14$ |
|15 | $-16p^2 - 30p + 25$ |
|16 | $7a^2 + 7a - 14$ |
|17 | $32n^2 - 8n - 12$ |
|18 | $-16n^2 + 8n + 48$ |
|19 | $35m^2 + 33m - 8$ |
|20 | $-7n^2 + 58n - 16$ |

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