Question

prove in written paragrah that (a+b)² = a + 2ab + b²​

Answer 1

That is one nice way to remember.

But the formula comes from the commutative ,distributive laws of addition and multiplication.

Commutative Law - ab = ba and a + b = b + a

Distributive Law - a(b + c) = ab + ac .

Thus ,(a + b)^2 = (a + b) (a + b) --- by the definition of power of 2

= a(a + b) + b(a + b) --- by distributive law

= aa + ab + ba + bb --- by distributive law

= a^2 + ab + ba + b^2 ---by definition of power of 2

= a^2 + ab + ab + b^2 ----by commutative law of multiplication

= a^2 + 2ab + b^2

btw in your question you've written (a+b)² = a + 2ab + b²

but it wrong it should be (a+b)² = a² + 2ab + b²