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प्रश्न
Factorise the following:
(x2 + y2 - z2)2 - 4x2y2
उत्तर
(x2 + y2 - z2)2 - 4x2y2
= (x2 + y2 - z2)2 - (2xy)2
= (x2 + y2 - z2 - 2xy)(x2 + y2 - z2 + 2xy)
= [(x2 + y2 - 2xy) - z2][(x2 + y2 + 2xy) - z2]
= [(x - y)2 - z2][(x + y)2 - z2]
= [(x - y - z)(x - y + z)][(x + y - z)(x + y + z)]
= (x - y - z)(x - y + z)(x + y - z)(x + y + z).
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