To solve these problems, we need to multiply two binomials (expressions with two terms). We’ll use the
FOIL method — which stands for:
-
First
-
Outer
-
Inner
-
Last
This means we multiply each term in the first parentheses by each term in the second parentheses, then combine like terms.
Let’s go one by one.
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1. (x + 4)(x + 6)
- First: x × x = x²
- Outer: x × 6 = 6x
- Inner: 4 × x = 4x
- Last: 4 × 6 = 24
→ Combine: x² + 6x + 4x + 24 =
x² + 10x + 24
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2. (x – 9)(6x – 3)
- First: x × 6x = 6x²
- Outer: x × (-3) = -3x
- Inner: -9 × 6x = -54x
- Last: -9 × (-3) = 27
→ Combine: 6x² - 3x - 54x + 27 =
6x² - 57x + 27
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3. (x – 8)(6x + 5)
- First: x × 6x = 6x²
- Outer: x × 5 = 5x
- Inner: -8 × 6x = -48x
- Last: -8 × 5 = -40
→ Combine: 6x² + 5x - 48x - 40 =
6x² - 43x - 40
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4. (3x – 2)(x – 5)
- First: 3x × x = 3x²
- Outer: 3x × (-5) = -15x
- Inner: -2 × x = -2x
- Last: -2 × (-5) = 10
→ Combine: 3x² - 15x - 2x + 10 =
3x² - 17x + 10
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5. (4x + 7)(x + 9)
- First: 4x × x = 4x²
- Outer: 4x × 9 = 36x
- Inner: 7 × x = 7x
- Last: 7 × 9 = 63
→ Combine: 4x² + 36x + 7x + 63 =
4x² + 43x + 63
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6. (8x + 2)(9x + 6)
- First: 8x × 9x = 72x²
- Outer: 8x × 6 = 48x
- Inner: 2 × 9x = 18x
- Last: 2 × 6 = 12
→ Combine: 72x² + 48x + 18x + 12 =
72x² + 66x + 12
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7. (8x – 9)(4x + 2)
- First: 8x × 4x = 32x²
- Outer: 8x × 2 = 16x
- Inner: -9 × 4x = -36x
- Last: -9 × 2 = -18
→ Combine: 32x² + 16x - 36x - 18 =
32x² - 20x - 18
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8. (x + 6)(x – 3)
- First: x × x = x²
- Outer: x × (-3) = -3x
- Inner: 6 × x = 6x
- Last: 6 × (-3) = -18
→ Combine: x² - 3x + 6x - 18 =
x² + 3x - 18
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9. (x + 7)(x – 3)
- First: x × x = x²
- Outer: x × (-3) = -3x
- Inner: 7 × x = 7x
- Last: 7 × (-3) = -21
→ Combine: x² - 3x + 7x - 21 =
x² + 4x - 21
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10. (x – 6)(4x – 3)
- First: x × 4x = 4x²
- Outer: x × (-3) = -3x
- Inner: -6 × 4x = -24x
- Last: -6 × (-3) = 18
→ Combine: 4x² - 3x - 24x + 18 =
4x² - 27x + 18
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11. (x – 7)(9x + 2)
- First: x × 9x = 9x²
- Outer: x × 2 = 2x
- Inner: -7 × 9x = -63x
- Last: -7 × 2 = -14
→ Combine: 9x² + 2x - 63x - 14 =
9x² - 61x - 14
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12. (2x – 4)(x – 8)
- First: 2x × x = 2x²
- Outer: 2x × (-8) = -16x
- Inner: -4 × x = -4x
- Last: -4 × (-8) = 32
→ Combine: 2x² - 16x - 4x + 32 =
2x² - 20x + 32
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All answers are now calculated and verified.
Final Answer:
1. x² + 10x + 24
2. 6x² - 57x + 27
3. 6x² - 43x - 40
4. 3x² - 17x + 10
5. 4x² + 43x + 63
6. 72x² + 66x + 12
7. 32x² - 20x - 18
8. x² + 3x - 18
9. x² + 4x - 21
10. 4x² - 27x + 18
11. 9x² - 61x - 14
12. 2x² - 20x + 32
Parent Tip: Review the logic above to help your child master the concept of multiplying binomials worksheet.
