Q9 of 90 Page 33

Factorize:

(i) 64a3 + 27b3


(ii) 125x3 – 8y3

(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)


More from this chapter

All 90 →
8

Factorize :

27 – 125x3 – 135x + 225x2

 8

Factorize :

125x3 – 64y3 – 300x2y + 240xy2

 10

Verify that:

x3 + y3 + z3 – 3xyz = 1/2 (x + y + z)[(x – y)2 + (y – z)2 + (z – x)2]

 10

Verify that:

27a3 + b3 + c3 – 9abc = (3a + b + c)[3a2 + b2 + c2 – 3ab – bc – 3ac]