Finite Math Examples

$(5 x + y) \cdot 12$

Step 1

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

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

Step 2

Expand the summation.

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

Step 3

Simplify the exponents for each term of the expansion.

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

Step 4

Simplify each term.

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Step 4.1

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

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

Step 4.2

Simplify.

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

Step 4.3

Anything raised to $0$ is $1$ .

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

Step 4.4

Multiply $5$ by $1$ .

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

Step 4.5

Multiply ${(5 x)}^{0}$ by $1$ .

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

Step 4.6

Apply the product rule to $5 x$ .

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

Step 4.7

Anything raised to $0$ is $1$ .

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

Step 4.8

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

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

Step 4.9

Anything raised to $0$ is $1$ .

$5 x + 1 \cdot {(y)}^{1}$

Step 4.10

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

$5 x + {(y)}^{1}$

Step 4.11

Simplify.

$5 x + y$