In Rudin 1.21 he says the following in the midst of proving a theorem,(adsbygoogle = window.adsbygoogle || []).push({});

"The identity b[tex]^{n}[/tex] - a[tex]^{n}[/tex]= (b-a)(b[tex]^{n-1}[/tex] + b[tex]^{n-2}[/tex]a + ... + a[tex]^{n-1}[/tex]) yields the inequality

b[tex]^{n}[/tex] - a[tex]^{n}[/tex] < (b-a)nb[tex]^{n-1}[/tex] when 0 < a < b"

I can understand that it is less than, but I cannot understand how it is coming (yielding) from the identity.

Any explanation would be greatly appreciated.

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# Rudin 1.21

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