Question

factorise : (3x-4y) ^4 -- x^4​

Answer 1

${(3x - 4y)}^{4} - {x}^{4} \\ = {((3x - 4y) {}^{2}) }^{2} - {(x {}^{2} )}^{2} \\ = (( {3x - 4y)}^{2} + {x}^{2} )(( {3x - 4y)}^{2} - {x}^{2} ) \\ = (( {3x - 4y)}^{2} + {x}^{2} )(3x - 4y + x)(3x - 4y - x) \\ = (9 {x}^{2} - 24xy + 16 {y}^{2} + {x}^{2} )(4x - 4y)(2x - 4y) \\ = (10 {x}^{2} - 24xy + 16 {y}^{2} )4(x - y)2(x - 2y) \\ = 8(10 {x}^{2} - 24xy + 16 {y}^{2} )(x - y)(x - 2y)$

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