Finite Math Examples

$(w + 5) \cdot 11$

Step 1

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

$\sum_{k = 0}^{1} \frac{1!}{(1 - k)! k!} \cdot {(w)}^{1 - k} \cdot {(5)}^{k}$

Step 2

Expand the summation.

$\frac{1!}{(1 - 0)! 0!} {(w)}^{1 - 0} \cdot {(5)}^{0} + \frac{1!}{(1 - 1)! 1!} {(w)}^{1 - 1} \cdot {(5)}^{1}$

Step 3

Simplify the exponents for each term of the expansion.

$1 \cdot {(w)}^{1} \cdot {(5)}^{0} + 1 \cdot {(w)}^{0} \cdot {(5)}^{1}$

Step 4

Simplify each term.

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Step 4.1

Multiply ${(w)}^{1}$ by $1$ .

${(w)}^{1} \cdot {(5)}^{0} + 1 \cdot {(w)}^{0} \cdot {(5)}^{1}$

Step 4.2

Simplify.

$w \cdot {(5)}^{0} + 1 \cdot {(w)}^{0} \cdot {(5)}^{1}$

Step 4.3

Anything raised to $0$ is $1$ .

$w \cdot 1 + 1 \cdot {(w)}^{0} \cdot {(5)}^{1}$

Step 4.4

Multiply $w$ by $1$ .

$w + 1 \cdot {(w)}^{0} \cdot {(5)}^{1}$

Step 4.5

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

$w + {(w)}^{0} \cdot {(5)}^{1}$

Step 4.6

Anything raised to $0$ is $1$ .

$w + 1 \cdot {(5)}^{1}$

Step 4.7

Multiply ${(5)}^{1}$ by $1$ .

$w + {(5)}^{1}$

Step 4.8

Evaluate the exponent.

$w + 5$