Factorise:
x3 + 64
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Given,
⇒ x3 + 64
⇒ (x)3 + (4)3
By using the identity,
a3 + b3 = (a + b)(a2 - ab + b2)
⇒ (x + 4)(x2 - x × 4 + 42)
⇒ (x + 4)(x2 - 4x + 16)
Hence, x3 + 64 = (x + 4)(x2 - 4x + 16).
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Evaluate:
(i) (674)2 - (326)2
(ii) (18.6)2 - (1.4)2
(x4 + x2y2 + y4)
8a3 + 27b3
7a3 + 56b3