Square of Sum/Algebraic Proof 2

Theorem

$\forall x, y \in \R: \paren {x + y}^2 = x^2 + 2 x y + y^2$


Proof

Follows directly from the Binomial Theorem:

$\ds \forall n \in \Z_{\ge 0}: \paren {x + y}^n = \sum_{k \mathop = 0}^n \binom n k x^{n - k} y^k$

putting $n = 2$.

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 20$: Binomial Series: $20.5$
  • 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 22$: Taylor Series: Binomial Series: $22.5.$
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