Directions: Factor each polynomial completely.Write your final answer in the blank space below.
1. x³+ 27
2.8y³ - 27
3. 1 + x³y³
4. 64 - p⁶
5. -2m⁵ + 250m²
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Directions: Factor each polynomial completely.Write your final answer in the blank space below.
1. x³+ 27
2.8y³ - 27
3. 1 + x³y³
4. 64 - p⁶
5. -2m⁵ + 250m²
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Answer:
1. x³ + 27
x³ + 3³
(x + 3) × (x² - x × 3 + 3²)
= (x + 3) × (x² - 3x + 9)
2. 8y³ - 27
2³y³ - 3³
(2y)³ - 3³
(2y - 3) × (((2y)² + 2y × 3 + 3²)
= (2y - 3) × (4y² + 6y + 9)
3. 1 + x³y³
(1 + xy) × (1 - 1xy + x²y²)
= (1 + xy) × (1 - xy + x²y²)
4. 64 - p⁶
(8 - p³) × (8 + p³)
= (2 - p) × (4 + 2p + p²) × (2 + p) × (4 - 2p + p²)
5. -2m⁵ + 250m²
-2m² × (m³ - 125)
= -2m² × (m - 5) × (m² + 5m + 25)