Question

Proof of algebraic identity of a²-b²=(a+b) (a-b)

Answer 1

Heya !!!

$(a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ you \: \: can \: \: easily \: \: multiply \: \: the \: \: two \: \: bionomials \: \: a + b \: \: and \: \: a - b \: \: to \: \: get \: \: this \: \: identity \\ \\ (a + b)(a - b) = a(a - b) +b (a - b) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {a}^{2} - ab + ba - {b}^{2} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {a}^{2} - {b}^{2}$

Hence, proved.


Hope it helps.

Answer 2

To prove:- a² - b² = (a+b)(a-b)

proof:- On Taking RHS

=> (a+b)(a-b) = a(a-b) +b(a-b)

=> a² - ab +ab - b²

=> a²- b²

LHS = RHS

hence proved.