Algebraic Expansion/Examples/(x + 1)^2
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Example of Algebraic Expansion
The following is an algebraic expansion:
- $\paren {x + 1}^2 = x^2 + 2 x + 1$
Proof 1
Use Square of Sum:
- $\forall x, y \in \R: \paren {x + y}^2 = x^2 + 2 x y + y^2$
substituting $1$ for $y$.
$\blacksquare$
Proof 2
\(\ds \paren {x + 1}^2\) | \(=\) | \(\ds \paren {x + 1} \paren {x + 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds x \paren {x + 1} + 1 \paren {x + 1}\) | Distributive Property | |||||||||||
\(\ds \) | \(=\) | \(\ds x^2 + 2 x + 1\) | Distributive Property |
$\blacksquare$