Algebraic Expansion/Examples/(x + 1)^3/Proof 2
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Example of Algebraic Expansion
- $\paren {x + 1}^3 = x^3 + 3 x^2 + 3 x + 1$
Proof
| \(\ds \paren {x + 1}^3\) | \(=\) | \(\ds \paren {x + 1} \paren {x^2 + 2 x + 1}\) | Algebraic Expansion: $\paren {x + 1}^2$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds x \paren {x^2 + 2 x + 1} + 1 \paren {x^2 + 2 x + 1}\) | Distributive Property | |||||||||||
| \(\ds \) | \(=\) | \(\ds x^3 + 3 x^2 + 3 x + 1\) | Distributive Property |
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): expansion
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): expansion: 1.