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Math Help - Prove that {IIxII + IIyII}^2 = IIxII^2 + 2*IIxII*IIyII + IIyII^2

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    Prove that {IIxII + IIyII}^2 = IIxII^2 + 2*IIxII*IIyII + IIyII^2

    Prove that {IIxII + IIyII}^2 = IIxII^2 + 2*IIxII*IIyII + IIyII^2 if x and y are elements of a vector space R!?
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  2. #2
    MHF Contributor arbolis's Avatar
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    Well that's very easy.
    Let the norm of x be definied such as \|x\| := \sqrt{\langle x,x\rangle} where \langle , \rangle is an inner product.
    So you have \left (\sqrt{\langle x,x\rangle}+\sqrt{\langle y,y\rangle}\right)^2. It is simply equal to \langle x,x\rangle+2\cdot \sqrt{\langle x,x\rangle}\cdot \sqrt {\langle y,y\rangle}+ \langle y,y\rangle which is equal to what you had to prove.
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