Let’s solve each problem step by step. We’ll use the distributive property (also called “FOIL” for binomials) and combine like terms where needed.
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1. x × (x + 6)
Distribute x to both terms inside:
= x·x + x·6
= x² + 6x
✔ Final:
x² + 6x
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2. y (2y - 6)
Distribute y:
= y·2y - y·6
= 2y² - 6y
✔ Final:
2y² - 6y
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3. (x - 1) × x
Same as x(x - 1):
= x·x - x·1
= x² - x
✔ Final:
x² - x
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4. (x - 3)(x + 3)
This is a difference of squares: (a - b)(a + b) = a² - b²
Here, a = x, b = 3
= x² - 9
✔ Final:
x² - 9
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5. (2x - 3) × 8
Distribute 8:
= 8·2x - 8·3
= 16x - 24
✔ Final:
16x - 24
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6. (x + 3)(x + 4)
Use FOIL:
First: x·x = x²
Outer: x·4 = 4x
Inner: 3·x = 3x
Last: 3·4 = 12
Combine: x² + 4x + 3x + 12 = x² + 7x + 12
✔ Final:
x² + 7x + 12
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7. (x - 2)(x - 9)
FOIL:
First: x·x = x²
Outer: x·(-9) = -9x
Inner: (-2)·x = -2x
Last: (-2)·(-9) = +18
Combine: x² - 9x - 2x + 18 = x² - 11x + 18
✔ Final:
x² - 11x + 18
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8. (y + 2)(y + 2)
This is (y + 2)² → perfect square trinomial
= y² + 2·y·2 + 2²
= y² + 4y + 4
Or via FOIL:
y·y = y²
y·2 = 2y
2·y = 2y
2·2 = 4
→ y² + 4y + 4
✔ Final:
y² + 4y + 4
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9. (x - 1)(4x + 1)
FOIL:
First: x·4x = 4x²
Outer: x·1 = x
Inner: (-1)·4x = -4x
Last: (-1)·1 = -1
Combine: 4x² + x - 4x - 1 = 4x² - 3x - 1
✔ Final:
4x² - 3x - 1
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10. (3x - 1)(2x + 3)
FOIL:
First: 3x·2x = 6x²
Outer: 3x·3 = 9x
Inner: (-1)·2x = -2x
Last: (-1)·3 = -3
Combine: 6x² + 9x - 2x - 3 = 6x² + 7x - 3
✔ Final:
6x² + 7x - 3
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Final Answer:
1. x² + 6x
2. 2y² - 6y
3. x² - x
4. x² - 9
5. 16x - 24
6. x² + 7x + 12
7. x² - 11x + 18
8. y² + 4y + 4
9. 4x² - 3x - 1
10. 6x² + 7x - 3
Parent Tip: Review the logic above to help your child master the concept of multiplying polynomials worksheet.
