Thread: interesting ....exponents and powers

think................if ( a+b ) the whole square =a square + b square + 2ab
THEN (a+b)the whole cube =?

something else ..............................if you could get this,please explain.

(a+b)^3=a^3+3a^2*b+3a*b^2+b^3
the pattern of the coefficient:
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
......
the pattern of the exponents :
the exponent of the a from n , decrease 1 each time to 0
the exponent of the b from 0 , increase 1 each time to n

(a+b)the whole square=aSQUARE+bSQUARE+2ab

answer............................................ ...........
(a+b)the whole cube=aCUBE+bCUBE+2aSQUAREb+2bSQUAREa

(a+b)2 = (a2 + b2 + 2ab)

Then

(a+b)3 = (a+b) x (a2 + b2 + 2ab)
= (a3 + 3ab2 + 3a2b + b3

Explanation:

When multiplying with brackets - take each part of the lefthand side and multiply the right.

(a+b) x (a2 + b2 + 2ab)
= a x (a2 + b2 + 2ab) + b x (a2 + b2 + 2ab)

I hope this helps

Originally Posted by pickbrain

think................if ( a+b ) the whole square =a square + b square + 2ab
THEN (a+b)the whole cube =?

something else ..............................if you could get this,please explain.