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प्रश्न
Factorize x4 + x2 y2 + y4
उत्तर
Adding x2 y2 and subtracting x2 y2 to the given equation.
= x4 + x2 y2 + y4 + x2 y2 - x2 y2
= x4 + 2x2 y2 + y4 - x2 y2
= (x2 )2 + 2 x x2 x y2 + ( y2 )2 - ( xy)2
Using identity a2 + 2ab + b2 = (a + b)2
= (x2 + y2 )2 - ( xy)2
Using identity a2 - b2 = (a + b)(a - b)
= (x2 + y2 + xy)(x2 + y2 - xy )
∴ x4 + x2 y2 + y4 = (x2 + y2 + xy)(x2 + y2 - xy)
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