Question

Proof that :

• ( a + b )² = a² + 2ab + b²

No spam (=｀ェ´=)​

Answer 1

(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)

Answer 2

Answer:

( a + b )² = a² + 2ab + b²

= a(a + b) + b(a + b)

= a² - ab + ba + b²

= a² + 2ab + b²