Pre-Algebra Worksheets | Monomials and Polynomials Worksheets - Free Printable

Let's solve each of the problems on the worksheet step by step. The task is to multiply binomials (two-term polynomials), which involves using the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last).

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1) (q + 6)(q - 4)

Use FOIL:

- F: $ q \cdot q = q^2 $
- O: $ q \cdot (-4) = -4q $
- I: $ 6 \cdot q = 6q $
- L: $ 6 \cdot (-4) = -24 $

Now combine:
$ q^2 - 4q + 6q - 24 = q^2 + 2q - 24 $

✔ Answer: $ q^2 + 2q - 24 $

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2) (s + 2)(5s + 9)

FOIL:

- F: $ s \cdot 5s = 5s^2 $
- O: $ s \cdot 9 = 9s $
- I: $ 2 \cdot 5s = 10s $
- L: $ 2 \cdot 9 = 18 $

Combine:
$ 5s^2 + 9s + 10s + 18 = 5s^2 + 19s + 18 $

✔ Answer: $ 5s^2 + 19s + 18 $

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3) (5c + 9)(c + 4)

FOIL:

- F: $ 5c \cdot c = 5c^2 $
- O: $ 5c \cdot 4 = 20c $
- I: $ 9 \cdot c = 9c $
- L: $ 9 \cdot 4 = 36 $

Combine:
$ 5c^2 + 20c + 9c + 36 = 5c^2 + 29c + 36 $

✔ Answer: $ 5c^2 + 29c + 36 $

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4) (3k + 5)(7k + 8)

FOIL:

- F: $ 3k \cdot 7k = 21k^2 $
- O: $ 3k \cdot 8 = 24k $
- I: $ 5 \cdot 7k = 35k $
- L: $ 5 \cdot 8 = 40 $

Combine:
$ 21k^2 + 24k + 35k + 40 = 21k^2 + 59k + 40 $

✔ Answer: $ 21k^2 + 59k + 40 $

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5) (s - 7)(s - 3)

FOIL:

- F: $ s \cdot s = s^2 $
- O: $ s \cdot (-3) = -3s $
- I: $ -7 \cdot s = -7s $
- L: $ -7 \cdot (-3) = 21 $

Combine:
$ s^2 - 3s - 7s + 21 = s^2 - 10s + 21 $

✔ Answer: $ s^2 - 10s + 21 $

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6) (d - 5)(4d - 8)

FOIL:

- F: $ d \cdot 4d = 4d^2 $
- O: $ d \cdot (-8) = -8d $
- I: $ -5 \cdot 4d = -20d $
- L: $ -5 \cdot (-8) = 40 $

Combine:
$ 4d^2 - 8d - 20d + 40 = 4d^2 - 28d + 40 $

✔ Answer: $ 4d^2 - 28d + 40 $

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7) (7y - 9)(y - 5)

FOIL:

- F: $ 7y \cdot y = 7y^2 $
- O: $ 7y \cdot (-5) = -35y $
- I: $ -9 \cdot y = -9y $
- L: $ -9 \cdot (-5) = 45 $

Combine:
$ 7y^2 - 35y - 9y + 45 = 7y^2 - 44y + 45 $

✔ Answer: $ 7y^2 - 44y + 45 $

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8) (2r - 3)(9r - 6)

FOIL:

- F: $ 2r \cdot 9r = 18r^2 $
- O: $ 2r \cdot (-6) = -12r $
- I: $ -3 \cdot 9r = -27r $
- L: $ -3 \cdot (-6) = 18 $

Combine:
$ 18r^2 - 12r - 27r + 18 = 18r^2 - 39r + 18 $

✔ Answer: $ 18r^2 - 39r + 18 $

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9) (g + 4)(g - 9)

FOIL:

- F: $ g \cdot g = g^2 $
- O: $ g \cdot (-9) = -9g $
- I: $ 4 \cdot g = 4g $
- L: $ 4 \cdot (-9) = -36 $

Combine:
$ g^2 - 9g + 4g - 36 = g^2 - 5g - 36 $

✔ Answer: $ g^2 - 5g - 36 $

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10) (q + 4)(2q + 8)

FOIL:

- F: $ q \cdot 2q = 2q^2 $
- O: $ q \cdot 8 = 8q $
- I: $ 4 \cdot 2q = 8q $
- L: $ 4 \cdot 8 = 32 $

Combine:
$ 2q^2 + 8q + 8q + 32 = 2q^2 + 16q + 32 $

✔ Answer: $ 2q^2 + 16q + 32 $

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✔ Final Answers:

1) $ q^2 + 2q - 24 $
2) $ 5s^2 + 19s + 18 $
3) $ 5c^2 + 29c + 36 $
4) $ 21k^2 + 59k + 40 $
5) $ s^2 - 10s + 21 $
6) $ 4d^2 - 28d + 40 $
7) $ 7y^2 - 44y + 45 $
8) $ 18r^2 - 39r + 18 $
9) $ g^2 - 5g - 36 $
10) $ 2q^2 + 16q + 32 $

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💡 Tip: Always check for like terms and combine them after distributing. Also, be careful with signs, especially when multiplying negative numbers.

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