Question

factorise
x^4 - 16 y^4
xxx
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Answer 1

$\mathsf \red{Given \: equation : \: \: } \mathsf{ {x}^{4} - 16 {y}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \\ \mathsf \pink{Rewrite \: {x}^{4} \: as \: { {(x}^{2}) }^{2} \: \: and \: \: 16 {y}^{4} \: as \: { {(4y}^{2} )}^{2} } \\ \\ \mathsf{ = \: { ({x}^{2} )}^{2} - {( {4y}^{2} )}^{2} } \\ \\ \mathsf \red{it \: is \: in \: the \: form \: of \: following \: identity : \: \: } \\ \\ \boxed{\mathsf \blue{ {a}^{2} - {b}^{2} = (a + b).(a - b)}} \\ \\ \mathsf{so : \: \: \: ({x}^{2} + 4 {y}^{2} ) \: . \: ( {x}^{2} - 4 {y}^{2}) } \\ \\ \mathsf \red{Again \: \: ( {x}^{2} - 4 {y}^{2}) \: \: is \: in \: the \: form \: of \: {a}^{2} - {b}^{2} } \\ \\ \mathsf{( {x}^{2} + 4 {y}^{2}) \: . \: (x + 4y).(x - 4y) } \\ \\ \boxed{ \mathsf \green{{x}^{4} - 16 {y}^{4} =( {x}^{2} + 4 {y}^{2}) \: . \: (x + 4y).(x - 4y) }}$