0(a + b)2 = a2 + b2 + 2ab
(a – b)2 = a2 + b2 – 2ab
(a + b)2 = (a – b)2 + 4ab
a2 – b2 = (a – b) (a + b)
a3 + b3 = (a + b) (a2 – ab + b2)
a3 – b3 = (a – b) (a2 + ab + b2)
Rules of counting numbers
Sum of first n natural numbers = n*(n+1)/2
Sum of first n odd natural numbers = n2
Sum of first n even natural numbers = n(n + 1)
Sum of the squares of first n natural numbers = n(n 1)(2n 1)
