Factorize:
x4 + 5x2 + 9
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Given,
⇒ x4 + 5x2 + 9
⇒ (x2)2 + 6x2 - x2 + (3)2
⇒ (x2)2 + 6x2 + (3)2 - x2
⇒ (x2)2 + 2 × 3 × x2 + (3)2 - x2
⇒ (x2 + 3)2 - (x)2 [As, (a + b)2 = a2 + b2 + 2ab]
⇒ (x2 + 3 + x)(x2 + 3 - x).
Hence, x4 + 5x2 + 9 = (x2 + 3 + x)(x2 + 3 - x).
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9x4 - x2 - 12x - 36
a2 + b2 - c2 - d2 + 2ab - 2cd
(a2 - b2)(c2 - d2) - 4abcd