Simplify the following (a + b)2 + (a – b)2

(i) (a + b)² + (a – b)²

(ii) (a + b)² – (a – b)²

Answer :

(i) (a + b)² + (a – b)²

It can be written as

= (a² + b² + 2ab) + (a² +b² – 2ab)

By further calculation

= a² + b² + 2ab + a² + b² – 2ab

So we get

= 2a² + 2b²

Taking 2 as common

= 2 (a² + b²)

(ii) (a + b)² – (a – b)²

It can be written as

= (a² + b² + 2ab) – (a² + b² – 2ab)

By further calculation

= a² + b² + 2ab – a² – b² + 2ab

So we get

= 4ab

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