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Question
Factorise:
`x^4 + y^4 - 27x^2y^2`
Solution
`x^4 + y^4 - 27x^2y^2`
= `(x^2)^2 + (y^2)^2 - 2x^2y^2 - 25x^2y^2`
= `(x^2 - y^2)^2 - 25x^2y^2`
= `( x^2 - y^2 )^2 - (5xy)^2` ...[∵ a2 - b2 = (a + b)(a - b)]
= `[ (x^2 - y^2 ) + 5xy ][( x^2 - y^2 ) - 5xy]`
= `[ x^2 + 5xy - y^2 ][ x^2 - 5xy - y^2 ]`
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