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Factorisation of Algebraic Expressions — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsFactorisation of Algebraic Expressions3 Marks
Question
Factorise: $24 a^3+81 b^3$
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Answer

24a³ + 81b³
…[Taking out the common factor 3]
= 3 [(2a)³ + (3b)³]
Here, A = 2a and B = 3b
∴ 24a³ + 81b³
= 3 {(2a + 3b) [(2a)² – (2a)(3b) + (3b)²]}
…[∵ A³ + B³ = (A + B) (A² – AB + B²)]
= 3(2a + 3b)(4a² – 6ab + 9b²)

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