Let’s solve each problem using FOIL (First, Outer, Inner, Last). I’ll go one by one and check my work carefully.
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Problem 1: (4x – 5)(x – 3)
F: 4x * x = 4x²
O: 4x * (-3) = -12x
I: -5 * x = -5x
L: -5 * (-3) = +15
Combine: 4x² -12x -5x +15 →
4x² -17x +15
✔ Check: Yes, -12x -5x = -17x. Correct.
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Problem 2: (4x – 4)(x – 4)
F: 4x * x = 4x²
O: 4x * (-4) = -16x
I: -4 * x = -4x
L: -4 * (-4) = +16
Combine: 4x² -16x -4x +16 →
4x² -20x +16
✔ Check: -16x -4x = -20x. Correct.
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Problem 3: (2x + 2)(3x + 5)
F: 2x * 3x = 6x²
O: 2x * 5 = 10x
I: 2 * 3x = 6x
L: 2 * 5 = 10
Combine: 6x² +10x +6x +10 →
6x² +16x +10
✔ Check: 10x +6x = 16x. Correct.
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Problem 4: (4x – 2)(3x + 3)
F: 4x * 3x = 12x²
O: 4x * 3 = 12x
I: -2 * 3x = -6x
L: -2 * 3 = -6
Combine: 12x² +12x -6x -6 →
12x² +6x -6
✔ Check: 12x -6x = 6x. Correct.
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Problem 5: (x – 1)(2x + 5)
F: x * 2x = 2x²
O: x * 5 = 5x
I: -1 * 2x = -2x
L: -1 * 5 = -5
Combine: 2x² +5x -2x -5 →
2x² +3x -5
✔ Check: 5x -2x = 3x. Correct.
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Problem 6: (5x + 2)(4x + 4)
F: 5x * 4x = 20x²
O: 5x * 4 = 20x
I: 2 * 4x = 8x
L: 2 * 4 = 8
Combine: 20x² +20x +8x +8 →
20x² +28x +8
✔ Check: 20x +8x = 28x. Correct.
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Problem 7: (3x – 3)(x – 2)
F: 3x * x = 3x²
O: 3x * (-2) = -6x
I: -3 * x = -3x
L: -3 * (-2) = +6
Combine: 3x² -6x -3x +6 →
3x² -9x +6
✔ Check: -6x -3x = -9x. Correct.
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Problem 8: (4x + 1)(3x + 2)
F: 4x * 3x = 12x²
O: 4x * 2 = 8x
I: 1 * 3x = 3x
L: 1 * 2 = 2
Combine: 12x² +8x +3x +2 →
12x² +11x +2
✔ Check: 8x +3x = 11x. Correct.
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Problem 9: (5x + 3)(3x + 4)
F: 5x * 3x = 15x²
O: 5x * 4 = 20x
I: 3 * 3x = 9x
L: 3 * 4 = 12
Combine: 15x² +20x +9x +12 →
15x² +29x +12
✔ Check: 20x +9x = 29x. Correct.
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Problem 10: (3x – 3)(3x + 2)
F: 3x * 3x = 9x²
O: 3x * 2 = 6x
I: -3 * 3x = -9x
L: -3 * 2 = -6
Combine: 9x² +6x -9x -6 →
9x² -3x -6
✔ Check: 6x -9x = -3x. Correct.
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Final Answer:
1. 4x² - 17x + 15
2. 4x² - 20x + 16
3. 6x² + 16x + 10
4. 12x² + 6x - 6
5. 2x² + 3x - 5
6. 20x² + 28x + 8
7. 3x² - 9x + 6
8. 12x² + 11x + 2
9. 15x² + 29x + 12
10. 9x² - 3x - 6
Parent Tip: Review the logic above to help your child master the concept of multiplying binomials worksheet with answers pdf.
