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Choose the correct factorisation of \(64x^3-27y^3\).\(64x^3-27y^3\) का सही गुणनखंडों में निरूपण चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((4x-3y)(16x^2+12xy+9y^2)\)\((4x-3y)(16x^2+12xy+9y^2)\)
Use the identity \(a^3-b^3=(a-b)(a^2+ab+b^2)\). Here \(64x^3=(4x)^3\) and \(27y^3=(3y)^3\). So \(64x^3-27y^3=(4x-3y)\big((4x)^2+(4x)(3y)+(3y)^2\big)\). Compute: \((4x)^2=16x^2\), \((4x)(3y)=12xy\), \((3y)^2=9y^2\). Hence \(64x^3-27y^3=(4x-3y)(16x^2+12xy+9y^2)\).पहचान \(a^3-b^3=(a-b)(a^2+ab+b^2)\) का उपयोग करें। यहाँ \(64x^3=(4x)^3\) और \(27y^3=(3y)^3\). इसलिए \(64x^3-27y^3=(4x-3y)\big((4x)^2+(4x)(3y)+(3y)^2\big)\). अब \((4x)^2=16x^2\), \((4x)(3y)=12xy\), \((3y)^2=9y^2\). अतः \(64x^3-27y^3=(4x-3y)(16x^2+12xy+9y^2)\).
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