Question

factorise x^4+y^4- 27x^2y^2
please answer it urgently​

Answer 1

We have,

$\quad {x}^{4} + {y}^{4} - 27 {x}^{2} {y}^{2} \\ \\ = {x}^{4} + {y}^{4} - 2 {x}^{2} {y}^{2} - 25 {x}^{2} {y}^{2} \\ \\ = { \left( {x}^{2} \right)}^{2} + { \left( {y}^{2} \right)}^{2} - 2 \left( {x}^{2} \right) \left( {y}^{2} \right) - 25 {x}^{2} {y}^{2} \\ \\ = { \left( {x}^{2} + {y}^{2} \right)}^{2} - 25 {x}^{2} {y}^{2} \\ \\ = { \left( {x}^{2} + {y}^{2} \right)}^{2} - {(5xy)}^{2} \\ \\ = \underline{ \boxed{( {x}^{2} + {y}^{2} - 5xy)( {x}^{2} + {y}^{2} + 5xy)}}$


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