Question

could explain how
$(a - b) { }^{2} = (a + b) {}^{ { }^{2} } - 4ab$
​

Answer 1

$rhs \\ \: \: \: {(a + b)}^{2} - 4ab \\ = {a}^{2} + {b}^{2} + 2ab - 4ab \\ = {a}^{2} + {b}^{2} - 2ab \\ = {(a - b)}^{2} lhs$

Answer 2

Solution :

Given , $(a - b) { }^{2} = (a + b) {}^{ { }^{2} } - 4ab$

Let's Solve Right Hand Side i.e RHS term

( a + b )² - 4ab

↪ a² + b² + 2ab - 4ab [ ∵ ( a+b)² = a² + b² + 2ab ]

↪ a² + b² - 2ab

↪( a - b )². [ ∵ ( a - b)² = a² + b² - 2ab ]

↪( a - b )² = LHS

It's Proved

Some Important Formula :

(I) ( a - b)² = a² + b² - 2ab

(ii) ( a+b)² = a² + b² + 2ab