Algebra Examples

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

Step 1

Pascal's Triangle can be displayed as such:

$1$

The triangle can be used to calculate the coefficients of the expansion of ${(a + b)}^{n}$ by taking the exponent $n$ and adding $1$ . The coefficients will correspond with line $n + 1$ of the triangle. For ${(x + y)}^{0}$ , $n = 0$ so the coefficients of the expansion will correspond with line $1$ .

Step 2

The expansion follows the rule ${(a + b)}^{n} = c_{0} a^{n} b^{0} + c_{1} a^{n - 1} b^{1} + c_{n - 1} a^{1} b^{n - 1} + c_{n} a^{0} b^{n}$ . The values of the coefficients, from the triangle, are $1$ .

$1 a^{0} b^{0}$

Step 3

Substitute the actual values of $a$ $x$ and $b$ $y$ into the expression.

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

Anything raised to $0$ is $1$ .

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

Step 4.3

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

${(y)}^{0}$

Step 4.4

Anything raised to $0$ is $1$ .

$1$