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Choose the correct factorisation of \(27p^3-64q^3\).\(27p^3-64q^3\) का सही गुणनखंडन चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((3p-4q)(9p^2+12pq+16q^2)\)\((3p-4q)(9p^2+12pq+16q^2)\)
Use \(a^3-b^3=(a-b)(a^2+ab+b^2)\). Here \(27p^3=(3p)^3\) and \(64q^3=(4q)^3\). So
\(27p^3-64q^3=(3p)^3-(4q)^3=(3p-4q)\big((3p)^2+(3p)(4q)+(4q)^2\big)\)
\(=(3p-4q)(9p^2+12pq+16q^2)\).\(a^3-b^3=(a-b)(a^2+ab+b^2)\) पहचान का प्रयोग करें। यहाँ \(27p^3=(3p)^3\) और \(64q^3=(4q)^3\) है। अतः
\(27p^3-64q^3=(3p)^3-(4q)^3=(3p-4q)\big((3p)^2+(3p)(4q)+(4q)^2\big)\)
\(=(3p-4q)(9p^2+12pq+16q^2)\)।
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