m³ + 8m²n + 19mn² + 12n³ এর উৎপাদক নিচের কোনটি?
Solution
Correct Answer: Option D
m³ + 8m²n + 19mn² + 12n³
= m³ + m²n + 7m²n + 7mn² + 12mn² + 12n³
= m²(m + n) + 7mn(m + n) + 12n²(m + n)
= (m + n)(m² + 7mn + 12n²)
= (m + n)(m² + 3mn + 4mn + 12n²)
= (m + n){m(m + 3n) + 4n(m + 3n)}
= (m + n)(m + 3n)(m + 4n)
= m³ + m²n + 7m²n + 7mn² + 12mn² + 12n³
= m²(m + n) + 7mn(m + n) + 12n²(m + n)
= (m + n)(m² + 7mn + 12n²)
= (m + n)(m² + 3mn + 4mn + 12n²)
= (m + n){m(m + 3n) + 4n(m + 3n)}
= (m + n)(m + 3n)(m + 4n)
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