Inner product/K/Norm/Parallelogram law/Exercise

Let ${}V$ denote a vector space over ${}{\mathbb {K} }$, endowed with an inner product ${}\left\langle -,-\right\rangle$. Let ${}\Vert {-}\Vert$ denote the associated norm. Show that the so-called Parallelogram law holds, that is,

${}\Vert {v+w}\Vert ^{2}+\Vert {v-w}\Vert ^{2}=2\Vert {v}\Vert ^{2}+2\Vert {w}\Vert ^{2}\,.$

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