Question

Factorisation

i)3a^3+4a-3

ii)1/8a^3+8/b^3​

Answer 1

Given : 1/8a^3+8/b^3​

To find :  Factorize

Solution:

1/8a^3+8/b^3​  

= 1/8a³  + 8/b³

= (1/2a)³  + (2/b)³

using x³ + y³  = ( x + y) ( x² + y² - xy)

x = 1/2a

y = 2/b

= ( 1/2a  + 2/b)  ( (1/2a)²  + (2/b)²  - (1/2a)(2/b) )

= ( 1/2a  + 2/b) ( (1/4a²  + 4/b²  - 1/ab )  

1/8a³  + 8/b³  = ( 1/2a  + 2/b) ( (1/4a²  + 4/b²  - 1/ab )  

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