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Which is the correct factorisation of \(8x^3+27\)?\(8x^3+27\) का सही गुणनखंडन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((2x+3)(4x^2-6x+9)\)\((2x+3)(4x^2-6x+9)\)
Use the sum of cubes identity \(a^3+b^3=(a+b)(a^2-ab+b^2)\). Here \(8x^3=(2x)^3\) and \(27=3^3\). So
\(8x^3+27=(2x)^3+3^3=(2x+3)((2x)^2-(2x)(3)+3^2)\)
\(=(2x+3)(4x^2-6x+9)\).घन के योग की पहचान \(a^3+b^3=(a+b)(a^2-ab+b^2)\) का प्रयोग करें। यहाँ \(8x^3=(2x)^3\) और \(27=3^3\) है। अतः
\(8x^3+27=(2x)^3+3^3=(2x+3)((2x)^2-(2x)(3)+3^2)\)
\(=(2x+3)(4x^2-6x+9)\)।
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