Multiplying Binomials worksheets - Free Printable

Let's solve each of these binomial multiplication problems step by step using the FOIL method (First, Outer, Inner, Last), which is a technique for multiplying two binomials.

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1) (3n + 2)(n + 3)

- F: $3n \cdot n = 3n^2$
- O: $3n \cdot 3 = 9n$
- I: $2 \cdot n = 2n$
- L: $2 \cdot 3 = 6$
Add: $3n^2 + 9n + 2n + 6 = 3n^2 + 11n + 6$

✔ Answer: $3n^2 + 11n + 6$

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2) (3p - 3)(p - 1)

- F: $3p \cdot p = 3p^2$
- O: $3p \cdot (-1) = -3p$
- I: $-3 \cdot p = -3p$
- L: $-3 \cdot (-1) = 3$
Add: $3p^2 - 3p - 3p + 3 = 3p^2 - 6p + 3$

✔ Answer: $3p^2 - 6p + 3$

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3) (2x + 1)(x - 1)

- F: $2x \cdot x = 2x^2$
- O: $2x \cdot (-1) = -2x$
- I: $1 \cdot x = x$
- L: $1 \cdot (-1) = -1$
Add: $2x^2 - 2x + x - 1 = 2x^2 - x - 1$

✔ Answer: $2x^2 - x - 1$

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4) (5x - 2)(5x - 8)

- F: $5x \cdot 5x = 25x^2$
- O: $5x \cdot (-8) = -40x$
- I: $-2 \cdot 5x = -10x$
- L: $-2 \cdot (-8) = 16$
Add: $25x^2 - 40x - 10x + 16 = 25x^2 - 50x + 16$

✔ Answer: $25x^2 - 50x + 16$

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5) (5v + 4)(3v - 6)

- F: $5v \cdot 3v = 15v^2$
- O: $5v \cdot (-6) = -30v$
- I: $4 \cdot 3v = 12v$
- L: $4 \cdot (-6) = -24$
Add: $15v^2 - 30v + 12v - 24 = 15v^2 - 18v - 24$

✔ Answer: $15v^2 - 18v - 24$

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6) (x + 1)(x + 2)

- F: $x \cdot x = x^2$
- O: $x \cdot 2 = 2x$
- I: $1 \cdot x = x$
- L: $1 \cdot 2 = 2$
Add: $x^2 + 2x + x + 2 = x^2 + 3x + 2$

✔ Answer: $x^2 + 3x + 2$

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7) (x - 5)(x - 4)

- F: $x \cdot x = x^2$
- O: $x \cdot (-4) = -4x$
- I: $-5 \cdot x = -5x$
- L: $-5 \cdot (-4) = 20$
Add: $x^2 - 4x - 5x + 20 = x^2 - 9x + 20$

✔ Answer: $x^2 - 9x + 20$

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8) (x + 5)(3x - 1)

- F: $x \cdot 3x = 3x^2$
- O: $x \cdot (-1) = -x$
- I: $5 \cdot 3x = 15x$
- L: $5 \cdot (-1) = -5$
Add: $3x^2 - x + 15x - 5 = 3x^2 + 14x - 5$

✔ Answer: $3x^2 + 14x - 5$

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9) (3x - y)(x + 2y)

- F: $3x \cdot x = 3x^2$
- O: $3x \cdot 2y = 6xy$
- I: $-y \cdot x = -xy$
- L: $-y \cdot 2y = -2y^2$
Add: $3x^2 + 6xy - xy - 2y^2 = 3x^2 + 5xy - 2y^2$

✔ Answer: $3x^2 + 5xy - 2y^2$

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10) (4x - 5)(x - 3)

- F: $4x \cdot x = 4x^2$
- O: $4x \cdot (-3) = -12x$
- I: $-5 \cdot x = -5x$
- L: $-5 \cdot (-3) = 15$
Add: $4x^2 - 12x - 5x + 15 = 4x^2 - 17x + 15$

✔ Answer: $4x^2 - 17x + 15$

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11) (x - 1)(2x + 5)

- F: $x \cdot 2x = 2x^2$
- O: $x \cdot 5 = 5x$
- I: $-1 \cdot 2x = -2x$
- L: $-1 \cdot 5 = -5$
Add: $2x^2 + 5x - 2x - 5 = 2x^2 + 3x - 5$

✔ Answer: $2x^2 + 3x - 5$

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12) (3x - 3)(3x + 2)

- F: $3x \cdot 3x = 9x^2$
- O: $3x \cdot 2 = 6x$
- I: $-3 \cdot 3x = -9x$
- L: $-3 \cdot 2 = -6$
Add: $9x^2 + 6x - 9x - 6 = 9x^2 - 3x - 6$

✔ Answer: $9x^2 - 3x - 6$

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13) (6x + 2y)(6x - 2y)

This is a difference of squares: $(a + b)(a - b) = a^2 - b^2$
Here, $a = 6x$, $b = 2y$
So: $(6x)^2 - (2y)^2 = 36x^2 - 4y^2$

✔ Answer: $36x^2 - 4y^2$

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14) (5x - 7)(3x - 4)

- F: $5x \cdot 3x = 15x^2$
- O: $5x \cdot (-4) = -20x$
- I: $-7 \cdot 3x = -21x$
- L: $-7 \cdot (-4) = 28$
Add: $15x^2 - 20x - 21x + 28 = 15x^2 - 41x + 28$

✔ Answer: $15x^2 - 41x + 28$

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15) (-2x + 5)(x - 1)

- F: $-2x \cdot x = -2x^2$
- O: $-2x \cdot (-1) = 2x$
- I: $5 \cdot x = 5x$
- L: $5 \cdot (-1) = -5$
Add: $-2x^2 + 2x + 5x - 5 = -2x^2 + 7x - 5$

✔ Answer: $-2x^2 + 7x - 5$

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✔ Final Answers:

1. $3n^2 + 11n + 6$
2. $3p^2 - 6p + 3$
3. $2x^2 - x - 1$
4. $25x^2 - 50x + 16$
5. $15v^2 - 18v - 24$
6. $x^2 + 3x + 2$
7. $x^2 - 9x + 20$
8. $3x^2 + 14x - 5$
9. $3x^2 + 5xy - 2y^2$
10. $4x^2 - 17x + 15$
11. $2x^2 + 3x - 5$
12. $9x^2 - 3x - 6$
13. $36x^2 - 4y^2$
14. $15x^2 - 41x + 28$
15. $-2x^2 + 7x - 5$

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