Find the product of (2m + 3n) and (m^2 + 2mn + n^2 ) (With steps please!)
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Answer: 2m³ + 3n³ + 7m²n + 8mn²
Step-by-step explanation:
(2m + 3n) × (m² + 2mn + n²)
= 2m (m² + 2mn + n²) + 3n (m² + 2mn + n²)
= (2m . m² + 2m . 2mn + 2m . n²) + (3n . m² + 3n . 2mn + 3n . n²)
( the (.) denotes multiplication)
= (2m³ + 4m²n + 2mn²) + (3m²n + 6mn² + 3n³)
= 2m³ + 4m²n + 2mn² + 3m²n + 6mn² + 3n³
= 2m³ + 3n³ + (4m²n + 3m²n) + (2mn² + 6mn²)
= 2m³ + 3n³ + 7m²n + 8mn²
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