Binomial Theorem/Examples/4th Power of Difference
< Binomial Theorem | Examples(Redirected from Fourth Power of Difference)
Jump to navigation
Jump to search
Example of Use of Binomial Theorem
- $\paren {x - y}^4 = x^4 - 4 x^3 y + 6 x^2 y^2 - 4 x y^3 + y^4$
Proof
Follows directly from the Binomial Theorem:
- $\ds \forall n \in \Z_{\ge 0}: \paren {x + \paren {-y} }^n = \sum_{k \mathop = 0}^n \binom n k x^{n - k} \paren {-y}^k$
putting $n = 4$.
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 2$: Special Products and Factors: $2.6$