Without finding cubes, factorise and find the value of (1/4)3 + (1/3)3 - (7/12)3 ?

Asked by Vikas | 4th Jul, 2017, 10:10: AM

Expert Answer:

begin mathsize 16px style Let space straight a equals 1 fourth space and space straight b equals 1 third
Now comma
open parentheses 1 fourth close parentheses cubed plus open parentheses 1 third close parentheses cubed minus open parentheses 7 over 12 close parentheses cubed
equals open parentheses 1 fourth close parentheses cubed plus open parentheses 1 third close parentheses cubed minus open parentheses 1 fourth plus 1 third close parentheses cubed
equals straight a cubed plus straight b cubed minus open parentheses straight a plus straight b close parentheses cubed
equals straight a cubed plus straight b cubed minus open square brackets straight a cubed plus straight b cubed plus 3 ab open parentheses straight a plus straight b close parentheses close square brackets
equals straight a cubed plus straight b cubed minus straight a cubed minus straight b cubed minus 3 ab open parentheses straight a plus straight b close parentheses
equals negative 3 cross times 1 fourth cross times 1 third cross times open parentheses 1 fourth plus 1 third close parentheses
equals negative 1 fourth cross times 7 over 12
equals negative 7 over 48 end style

Answered by Rashmi Khot | 4th Jul, 2017, 11:47: AM