Q. 95.0( 1 Vote )

Factorize:

(i) 64a3 + 27b3

(ii) 125x3 – 8y3

Answer :

(i) 64 a3 + 27 b3


Using Formula : x3 + y3 = (x+ y) (x2 + y2 – xy)


64 a3 + 27 b3 = (4 a )3 + (3 b)3


64 a3 + 27 b3 = (4 a + 3 b) [ (4 a )2 + (3 b)2 + 4 a × 3 b]


64 a3 + 27 b3 = (4 a + 3 b) ( 16 a2 + 9 b2 + 12 ab)


(ii) 125 x3 – 8 y3


Using Formula : x3 - y3 = (x- y) (x2 + y2 + xy)


125 x3 – 8 y3 = (5 x)3 – (2 y)3


125 x3 – 8 y3 = (5 x – 2 y) [ (5 x )2 + (2 y )2 + 5 x × 2 y]


125 x3 – 8 y3 = (5 x – 2 y) (25 x2 + 4 y2 + 10 xy)


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