Expand Using the Binomial Theorem (x+y)^0

${(x + y)}^{0}$

Step 1

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

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

Step 2

Expand the summation.

$\frac{0!}{(0 - 0)! 0!} {(x)}^{0 - 0} \cdot {(y)}^{0}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(x)}^{0} \cdot {(y)}^{0}$

Step 4

Simplify the polynomial result.

Multiply ${(x)}^{0}$ by $1$ .

${(x)}^{0} \cdot {(y)}^{0}$

Anything raised to $0$ is $1$ .

$1 \cdot {(y)}^{0}$

Multiply ${(y)}^{0}$ by $1$ .

${(y)}^{0}$

Anything raised to $0$ is $1$ .

$1$