Question
Factorise:$x^4 + y^4 - 6x^2y^2$
✓
Answer
$x^4 + y^4 - 6x^2y^2$
$= (x^2)^2 + (y)^2 - 2x^2y^2 - 4x^2y^2$
$= [(x^2)^2 + (y)^2 - 2x^2y^2] - (4x^2y^2)$
$= (x^2 - y^2)^2 - (2xy)^2$
$= (x^2- y^2 - 2xy)(x^2 - y^2 + 2xy).$
$= (x^2)^2 + (y)^2 - 2x^2y^2 - 4x^2y^2$
$= [(x^2)^2 + (y)^2 - 2x^2y^2] - (4x^2y^2)$
$= (x^2 - y^2)^2 - (2xy)^2$
$= (x^2- y^2 - 2xy)(x^2 - y^2 + 2xy).$
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