FROM WHERE a^3 + b^3 formula is derived?

Asked by Ayush | 3rd Apr, 2015, 07:55: PM

Expert Answer:

C o n s i d e r space t w o space c u b e s space w i t h space s i d e s space a space a n d space b space r e p e c t i v e l y. L e t space u s space a s s u m e space t h a t space a greater than b. T h e n space a cubed space r e p r e s e n t s space t h e space v o l u m e space o f space t h e space b i g g e r space c u b e space a n d space b cubed space r e p r e s e n t s space t h e space v o l u m e space o f t h e space s m a l l e r space c u b e. N o w space w e space n e e d space t o space f i n d space t h e space v o l u m e s space o f space b o t h space t h e space c u b e s. B y space c o n s t r u c t i o n comma space e x t e n d space t h e space s i d e space o f space t h e space c u b e space b y space b. T h u s comma space t h e space l e n g t h space o f space t h e space n e w space c u b o i d space b e c o m e s space a plus b. T h e space b r e a d t h space a n d space h e i g h t space o f space t h e space c u b o i d space a r e space a space a n d space a. T h u s comma space t h e space V o l u m e space o f space t h e space c u b o i d space i s space open parentheses a plus b close parentheses a squared.... left parenthesis 1 right parenthesis T h e space v o l u m e space o f space t h e space c u b e s space w i t h space s i d e s space a space a n d space b equals a cubed plus b cubed.... left parenthesis 2 right parenthesis W e space k n o w space t h a t space t h e space s u m space o f space t h e space v o l u m e s space o f space t h e space t w o space c u b e s space i e q u a l space t o space t h e space d i f f e r e n c e space o f space v o l u m e s space o f space t h e space c u b o i d space a n d space t h e space a d d e d space v o l u m e space b y space c o n s t r u c t i o n...... left curly bracket s e e space t h e space d i a g r m right curly bracket H e n c e comma space a cubed plus b cubed equals open parentheses a plus b close parentheses a squared minus open square brackets a open parentheses a minus b close parentheses plus b open parentheses a minus b close parentheses close square brackets b rightwards double arrow space a cubed plus b cubed equals open parentheses a plus b close parentheses a squared minus open square brackets open parentheses a plus b close parentheses open parentheses a minus b close parentheses close square brackets b rightwards double arrow space a cubed plus b cubed equals open parentheses a plus b close parentheses open square brackets a squared minus a b plus b squared close square brackets

Answered by Vimala Ramamurthy | 4th Apr, 2015, 10:02: AM

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