Question

1. Show by commutative, associative and distributive laws that
(1) (a + b) = a + b + 2ab :
​

Answer 1

Answer:

(a+b)²

= (a+b)×(a+b)

= (a+b)(a+b)

= [a×(a+b)]+[b×(a+b)]

= [a(a+b)]+[b(a+b)]

= [{(a×a)+(a×b)}] + [{(b×a)+(b×b)}]

= [(a²)+(ab)] + [(ba)+(b²)]

= (a²)+(ab)+(ba)+(b²)

Since a×b = b×a (commutative property), ba = ab.

= (a²)+(ab)+(ab)+(b²)

= (a²)+(2×ab)+(b²)

= (a²)+(2ab)+(b²)