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Answer:
PRACTICE EXERCISE 1:
1. The first term is the cube of 4x
2. The second term is thrice the product of (4x)² and 5y
3. The third term is thrice the product of 4x and (5y)²
4. The fourth term is the cube of 5y
5. The first term is equal to 216m³
solution: (6m)³ = 216m³
6. The second term is equal to -324m²
solution: 3(6m)²(3)
(6m)² = 36m²
36m² × 3 = 108m²
108m² × 3 = 324m²
7. The third term is equal to 162m
solution: 3(6m)(3)²
(3)² = 9
6m × 9 = 54m
54m × 3 = 162m
8. The fourth term is equal to -27
solution: (3)³ = 27
PRACTICE EXERCISE 2:
1. (5d + 3)³
x³ = 125d³
3x²y = 225d²
3xy² = 135d
y³ = 27
125d³ + 225d² + 135d + 27
2. (4k - 9)³
x³ = 64k³
3x²y = 432k²
3xy² = 972k
y³ = 729
64k³ − 432k² + 972k − 729
3. (3 - 7x)³
x³ = 343x³
3x²y = 441x²
3xy² = 189x
343x³ + 441x² − 189x + 27
4. (2a² + 7b)³
x³ = 8a⁶
3x²y = 84a⁴b
3xy² = 294a²b²
y³ = 343b³
8a⁶+ 84a⁴b + 294a²b² +343b³
5. (3m + 2n)³
x³ = 27m³
3x²y = 54m²n
3xy² = 36mn²
y³ = 8n³
27m³ +54m²n + 36mn²+ 8n³
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Verified answer
Given
1.
2.
3.
4.
5.
=======================
Answer:
PRACTICE EXERCISE 1:
1. The first term is the cube of 4x
2. The second term is thrice the product of (4x)² and 5y
3. The third term is thrice the product of 4x and (5y)²
4. The fourth term is the cube of 5y
5. The first term is equal to 216m³
solution: (6m)³ = 216m³
6. The second term is equal to -324m²
solution: 3(6m)²(3)
(6m)² = 36m²
36m² × 3 = 108m²
108m² × 3 = 324m²
7. The third term is equal to 162m
solution: 3(6m)(3)²
(3)² = 9
6m × 9 = 54m
54m × 3 = 162m
8. The fourth term is equal to -27
solution: (3)³ = 27
PRACTICE EXERCISE 2:
1. (5d + 3)³
x³ = 125d³
3x²y = 225d²
3xy² = 135d
y³ = 27
125d³ + 225d² + 135d + 27
2. (4k - 9)³
x³ = 64k³
3x²y = 432k²
3xy² = 972k
y³ = 729
64k³ − 432k² + 972k − 729
3. (3 - 7x)³
x³ = 343x³
3x²y = 441x²
3xy² = 189x
y³ = 27
343x³ + 441x² − 189x + 27
4. (2a² + 7b)³
x³ = 8a⁶
3x²y = 84a⁴b
3xy² = 294a²b²
y³ = 343b³
8a⁶+ 84a⁴b + 294a²b² +343b³
5. (3m + 2n)³
x³ = 27m³
3x²y = 54m²n
3xy² = 36mn²
y³ = 8n³
27m³ +54m²n + 36mn²+ 8n³