Algebraic Expansion/Examples/(x + 1)^3
Example of Algebraic Expansion
The following is an algebraic expansion:
- $\paren {x + 1}^3 = x^3 + 3 x^2 + 3 x + 1$
Proof 1
This is Cube of Sum: Corollary.
$\blacksquare$
Proof 2
| \(\ds \paren {x + 1}^3\) | \(=\) | \(\ds \paren {x + 1} \paren {x^2 + 2 x + 1}\) | 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 |
$\blacksquare$