Let’s solve each problem step by step. We’re multiplying two binomials — that means two expressions with two terms, like (x + 3)(x + 5). We’ll use the FOIL method: First, Outer, Inner, Last.
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1. (x + 3)(x + 1)
First: x * x = x²
Outer: x * 1 = x
Inner: 3 * x = 3x
Last: 3 * 1 = 3
Add them: x² + x + 3x + 3 =
x² + 4x + 3
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2. (x + 5)(x + 2)
First: x * x = x²
Outer: x * 2 = 2x
Inner: 5 * x = 5x
Last: 5 * 2 = 10
Add them: x² + 2x + 5x + 10 =
x² + 7x + 10
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3. (x + 3)(x + 3) → This is (x+3)²
First: x * x = x²
Outer: x * 3 = 3x
Inner: 3 * x = 3x
Last: 3 * 3 = 9
Add them: x² + 3x + 3x + 9 =
x² + 6x + 9
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4. (x + 8)(x + 2)
First: x * x = x²
Outer: x * 2 = 2x
Inner: 8 * x = 8x
Last: 8 * 2 = 16
Add them: x² + 2x + 8x + 16 =
x² + 10x + 16
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5. (x - 4)(x + 2)
First: x * x = x²
Outer: x * 2 = 2x
Inner: -4 * x = -4x
Last: -4 * 2 = -8
Add them: x² + 2x - 4x - 8 =
x² - 2x - 8
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6. (x - 3)(x - 4)
First: x * x = x²
Outer: x * (-4) = -4x
Inner: -3 * x = -3x
Last: -3 * (-4) = 12
Add them: x² - 4x - 3x + 12 =
x² - 7x + 12
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7. (x + 4)(x - 5)
First: x * x = x²
Outer: x * (-5) = -5x
Inner: 4 * x = 4x
Last: 4 * (-5) = -20
Add them: x² - 5x + 4x - 20 =
x² - x - 20
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8. (x + 11)(x - 2)
First: x * x = x²
Outer: x * (-2) = -2x
Inner: 11 * x = 11x
Last: 11 * (-2) = -22
Add them: x² - 2x + 11x - 22 =
x² + 9x - 22
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9. (x + 8)(x + 1)
First: x * x = x²
Outer: x * 1 = x
Inner: 8 * x = 8x
Last: 8 * 1 = 8
Add them: x² + x + 8x + 8 =
x² + 9x + 8
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10. (x + 12)(x + 1)
First: x * x = x²
Outer: x * 1 = x
Inner: 12 * x = 12x
Last: 12 * 1 = 12
Add them: x² + x + 12x + 12 =
x² + 13x + 12
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Final Answer:
1. x² + 4x + 3
2. x² + 7x + 10
3. x² + 6x + 9
4. x² + 10x + 16
5. x² - 2x - 8
6. x² - 7x + 12
7. x² - x - 20
8. x² + 9x - 22
9. x² + 9x + 8
10. x² + 13x + 12
Parent Tip: Review the logic above to help your child master the concept of multiply binomials worksheet.
