Expand Using the Binomial Theorem (s+t)^9

${(s + t)}^{9}$

Use the binomial expansion theorem to find each term. The binomial theorem states ${(a + b)}^{n} = \sum_{k = 0}^{n} n C k \cdot (a^{n - k} b^{k})$ .

$\sum_{k = 0}^{9} \frac{9!}{(9 - k)! k!} \cdot {(s)}^{9 - k} \cdot {(t)}^{k}$

Expand the summation.

$\frac{9!}{(9 - 0)! 0!} {(s)}^{9 - 0} \cdot {(t)}^{0} + \frac{9!}{(9 - 1)! 1!} {(s)}^{9 - 1} \cdot {(t)}^{1} + \dots + \frac{9!}{(9 - 9)! 9!} {(s)}^{9 - 9} \cdot {(t)}^{9}$

Simplify the exponents for each term of the expansion.

$1 \cdot {(s)}^{9} \cdot {(t)}^{0} + 9 \cdot {(s)}^{8} \cdot {(t)}^{1} + \dots + 1 \cdot {(s)}^{0} \cdot {(t)}^{9}$

Simplify the polynomial result.

$s^{9} + 9 s^{8} t + 36 s^{7} t^{2} + 84 s^{6} t^{3} + 126 s^{5} t^{4} + 126 s^{4} t^{5} + 84 s^{3} t^{6} + 36 s^{2} t^{7} + 9 s t^{8} + t^{9}$

Expand Using the Binomial Theorem (s+t)^9

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