Finite Math Examples

$f (n) = n^{2} - 3 n$ , $f i n d f (5)$

Step 1

Apply the distributive property.

$(n^{2} i - 3 n i) n d (n^{2} - 3 n) \cdot 5$

Step 2

Apply the distributive property.

$(n^{2} i n - 3 n i n) d (n^{2} - 3 n) \cdot 5$

Step 3

Multiply $n^{2}$ by $n$ by adding the exponents.

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Step 3.1

Move $n$ .

$(n \cdot n^{2} i - 3 n i n) d (n^{2} - 3 n) \cdot 5$

Step 3.2

Multiply $n$ by $n^{2}$ .

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Step 3.2.1

Raise $n$ to the power of $1$ .

$(n^{1} n^{2} i - 3 n i n) d (n^{2} - 3 n) \cdot 5$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(n^{1 + 2} i - 3 n i n) d (n^{2} - 3 n) \cdot 5$

Step 3.3

Add $1$ and $2$ .

$(n^{3} i - 3 n i n) d (n^{2} - 3 n) \cdot 5$

Step 4

Multiply $n$ by $n$ by adding the exponents.

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Step 4.1

Move $n$ .

$(n^{3} i - 3 (n \cdot n) i) d (n^{2} - 3 n) \cdot 5$

Step 4.2

Multiply $n$ by $n$ .

$(n^{3} i - 3 n^{2} i) d (n^{2} - 3 n) \cdot 5$

Step 5

Apply the distributive property.

$(n^{3} i d - 3 n^{2} i d) (n^{2} - 3 n) \cdot 5$

Step 6

Expand $(n^{3} i d - 3 n^{2} i d) (n^{2} - 3 n)$ using the FOIL Method.

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Step 6.1

Apply the distributive property.

$(n^{3} i d (n^{2} - 3 n) - 3 n^{2} i d (n^{2} - 3 n)) \cdot 5$

Step 6.2

Apply the distributive property.

$(n^{3} i d n^{2} + n^{3} i d (- 3 n) - 3 n^{2} i d (n^{2} - 3 n)) \cdot 5$

Step 6.3

Apply the distributive property.

$(n^{3} i d n^{2} + n^{3} i d (- 3 n) - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7

Simplify and combine like terms.

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Step 7.1

Simplify each term.

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Step 7.1.1

Multiply $n^{3}$ by $n^{2}$ by adding the exponents.

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Step 7.1.1.1

Move $n^{2}$ .

$(n^{2} n^{3} i d + n^{3} i d (- 3 n) - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(n^{2 + 3} i d + n^{3} i d (- 3 n) - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.1.3

Add $2$ and $3$ .

$(n^{5} i d + n^{3} i d (- 3 n) - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.2

Multiply $n^{3}$ by $n$ by adding the exponents.

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Step 7.1.2.1

Move $n$ .

$(n^{5} i d + n \cdot n^{3} i d \cdot - 3 - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.2.2

Multiply $n$ by $n^{3}$ .

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Step 7.1.2.2.1

Raise $n$ to the power of $1$ .

$(n^{5} i d + n^{1} n^{3} i d \cdot - 3 - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(n^{5} i d + n^{1 + 3} i d \cdot - 3 - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.2.3

Add $1$ and $3$ .

$(n^{5} i d + n^{4} i d \cdot - 3 - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.3

Move $- 3$ to the left of $n^{4} i d$ .

$(n^{5} i d - 3 \cdot (n^{4} i d) - 3 n^{2} i d n^{2} - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.4

Multiply $n^{2}$ by $n^{2}$ by adding the exponents.

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Step 7.1.4.1

Move $n^{2}$ .

$(n^{5} i d - 3 n^{4} i d - 3 (n^{2} n^{2}) i d - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(n^{5} i d - 3 n^{4} i d - 3 n^{2 + 2} i d - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.4.3

Add $2$ and $2$ .

$(n^{5} i d - 3 n^{4} i d - 3 n^{4} i d - 3 n^{2} i d (- 3 n)) \cdot 5$

Step 7.1.5

Multiply $n^{2}$ by $n$ by adding the exponents.

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Step 7.1.5.1

Move $n$ .

$(n^{5} i d - 3 n^{4} i d - 3 n^{4} i d - 3 (n \cdot n^{2}) i d \cdot - 3) \cdot 5$

Step 7.1.5.2

Multiply $n$ by $n^{2}$ .

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Step 7.1.5.2.1

Raise $n$ to the power of $1$ .

$(n^{5} i d - 3 n^{4} i d - 3 n^{4} i d - 3 (n^{1} n^{2}) i d \cdot - 3) \cdot 5$

Step 7.1.5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(n^{5} i d - 3 n^{4} i d - 3 n^{4} i d - 3 n^{1 + 2} i d \cdot - 3) \cdot 5$

Step 7.1.5.3

Add $1$ and $2$ .

$(n^{5} i d - 3 n^{4} i d - 3 n^{4} i d - 3 n^{3} i d \cdot - 3) \cdot 5$

Step 7.1.6

Multiply $- 3$ by $- 3$ .

$(n^{5} i d - 3 n^{4} i d - 3 n^{4} i d + 9 n^{3} i d) \cdot 5$

Step 7.2

Subtract $3 n^{4} i d$ from $- 3 n^{4} i d$ .

$(n^{5} i d - 6 n^{4} i d + 9 n^{3} i d) \cdot 5$

Step 8

Apply the distributive property.

$n^{5} i d \cdot 5 - 6 n^{4} i d \cdot 5 + 9 n^{3} i d \cdot 5$

Step 9

Simplify.

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Step 9.1

Move $5$ to the left of $n^{5} i d$ .

$5 \cdot (n^{5} i d) - 6 n^{4} i d \cdot 5 + 9 n^{3} i d \cdot 5$

Step 9.2

Multiply $5$ by $- 6$ .

$5 \cdot (n^{5} i d) - 30 n^{4} i d + 9 n^{3} i d \cdot 5$

Step 9.3

Multiply $5$ by $9$ .

$5 \cdot (n^{5} i d) - 30 n^{4} i d + 45 n^{3} i d$

Step 10

Remove parentheses.

$5 n^{5} i d - 30 n^{4} i d + 45 n^{3} i d$

Step 11

Reorder.

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Step 11.1

Move $i$ .

$5 n^{5} d i - 30 n^{4} i d + 45 n^{3} i d$

Step 11.2

Move $n^{5}$ .

$5 d n^{5} i - 30 n^{4} i d + 45 n^{3} i d$

Step 11.3

Move $i$ .

$5 d n^{5} i - 30 n^{4} d i + 45 n^{3} i d$

Step 11.4

Move $n^{4}$ .

$5 d n^{5} i - 30 d n^{4} i + 45 n^{3} i d$

Step 11.5

Move $i$ .

$5 d n^{5} i - 30 d n^{4} i + 45 n^{3} d i$

Step 11.6

Move $n^{3}$ .

$5 d n^{5} i - 30 d n^{4} i + 45 d n^{3} i$