Factor ex ex2Solution ex ex 2 ex2 2exex ex2 a b2 a2

Solution

( e^x - e^-x )² = (e^x)² - 2.e^x.e^-x + (e^-x)² [ (a - b)² = a² - 2ab + b² ]

= e^2x - 2e^x-x + e^-2x [ (a^m)ⁿ = a^mn , a^m.aⁿ = a^m+n ]

= e^2x -2e⁰ + e^-2x

= e^2x - 2 + e^-2x [ since , e⁰ = 1 ]

= e^2x - 2 + e^-2x

Therefore ,

( e^x - e^-x )² = e^2x - 2 + e^-2x