Expand Using the Binomial Theorem (w+y)^8

${(w + y)}^{8}$

Step 1

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

$\sum_{k = 0}^{8} \frac{8!}{(8 - k)! k!} \cdot {(w)}^{8 - k} \cdot {(y)}^{k}$

Step 2

Expand the summation.

$\frac{8!}{(8 - 0)! 0!} {(w)}^{8 - 0} \cdot {(y)}^{0} + \frac{8!}{(8 - 1)! 1!} {(w)}^{8 - 1} \cdot {(y)}^{1} + \dots + \frac{8!}{(8 - 8)! 8!} {(w)}^{8 - 8} \cdot {(y)}^{8}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(w)}^{8} \cdot {(y)}^{0} + 8 \cdot {(w)}^{7} \cdot {(y)}^{1} + \dots + 1 \cdot {(w)}^{0} \cdot {(y)}^{8}$

Step 4

Simplify the polynomial result.

$w^{8} + 8 w^{7} y + 28 w^{6} y^{2} + 56 w^{5} y^{3} + 70 w^{4} y^{4} + 56 w^{3} y^{5} + 28 w^{2} y^{6} + 8 w y^{7} + y^{8}$

Expand Using the Binomial Theorem (w+y)^8

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