Question

(a) a2 + 2ab + b2, a2 - 2ab - b2, a2 + b2​

Answer 1

Answer:

= (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)

Without Algebra, proof that (a+b)² is not equal to a²+b²

Let a = 5, and b = 4.

In (a+b)²,

= (5+4)²

= (9)²

= 9×9

= 81,

Whereas in a² + b²

= 5² + 4²

= 25 + 16

= 41.