Finite Math Examples

$(7 n^{3} - \frac{21}{8} n^{2} - \frac{28}{5} n) (\frac{3}{7} n^{2})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $n^{2}$ and $\frac{21}{8}$ .

$(7 n^{3} - \frac{n^{2} \cdot 21}{8} - \frac{28}{5} n) (\frac{3}{7} n^{2})$

Step 1.1.2

Move $21$ to the left of $n^{2}$ .

$(7 n^{3} - \frac{21 \cdot n^{2}}{8} - \frac{28}{5} n) (\frac{3}{7} n^{2})$

Step 1.1.3

Combine $n$ and $\frac{28}{5}$ .

$(7 n^{3} - \frac{21 n^{2}}{8} - \frac{n \cdot 28}{5}) (\frac{3}{7} n^{2})$

Step 1.1.4

Move $28$ to the left of $n$ .

$(7 n^{3} - \frac{21 n^{2}}{8} - \frac{28 n}{5}) (\frac{3}{7} n^{2})$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $\frac{3}{7}$ and $n^{2}$ .

$(7 n^{3} - \frac{21 n^{2}}{8} - \frac{28 n}{5}) \frac{3 n^{2}}{7}$

Step 1.2.2

Apply the distributive property.

$7 n^{3} \frac{3 n^{2}}{7} - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3

Simplify.

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Step 1.3.1

Cancel the common factor of $7$ .

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Step 1.3.1.1

Factor $7$ out of $7 n^{3}$ .

$7 (n^{3}) \frac{3 n^{2}}{7} - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.1.2

Cancel the common factor.

$7 n^{3} \frac{3 n^{2}}{7} - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.1.3

Rewrite the expression.

$n^{3} (3 n^{2}) - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.2

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

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Step 1.3.2.1

Move $n^{2}$ .

$n^{2} n^{3} \cdot 3 - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.2.2

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

$n^{2 + 3} \cdot 3 - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.2.3

Add $2$ and $3$ .

$n^{5} \cdot 3 - \frac{21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.3

Cancel the common factor of $7$ .

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Step 1.3.3.1

Move the leading negative in $- \frac{21 n^{2}}{8}$ into the numerator.

$n^{5} \cdot 3 + \frac{- 21 n^{2}}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.3.2

Factor $7$ out of $- 21 n^{2}$ .

$n^{5} \cdot 3 + \frac{7 (- 3 n^{2})}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.3.3

Cancel the common factor.

$n^{5} \cdot 3 + \frac{7 (- 3 n^{2})}{8} \cdot \frac{3 n^{2}}{7} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.3.4

Rewrite the expression.

$n^{5} \cdot 3 + \frac{- 3 n^{2}}{8} (3 n^{2}) - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.4

Combine $3$ and $\frac{- 3 n^{2}}{8}$ .

$n^{5} \cdot 3 + \frac{3 (- 3 n^{2})}{8} n^{2} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.5

Multiply $- 3$ by $3$ .

$n^{5} \cdot 3 + \frac{- 9 n^{2}}{8} n^{2} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.6

Combine $\frac{- 9 n^{2}}{8}$ and $n^{2}$ .

$n^{5} \cdot 3 + \frac{- 9 n^{2} n^{2}}{8} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.7

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

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Step 1.3.7.1

Move $n^{2}$ .

$n^{5} \cdot 3 + \frac{- 9 (n^{2} n^{2})}{8} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.7.2

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

$n^{5} \cdot 3 + \frac{- 9 n^{2 + 2}}{8} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.7.3

Add $2$ and $2$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} - \frac{28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.8

Cancel the common factor of $7$ .

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Step 1.3.8.1

Move the leading negative in $- \frac{28 n}{5}$ into the numerator.

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 28 n}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.8.2

Factor $7$ out of $- 28 n$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{7 (- 4 n)}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.8.3

Cancel the common factor.

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{7 (- 4 n)}{5} \cdot \frac{3 n^{2}}{7}$

Step 1.3.8.4

Rewrite the expression.

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 4 n}{5} (3 n^{2})$

Step 1.3.9

Combine $3$ and $\frac{- 4 n}{5}$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{3 (- 4 n)}{5} n^{2}$

Step 1.3.10

Multiply $- 4$ by $3$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 12 n}{5} n^{2}$

Step 1.3.11

Combine $\frac{- 12 n}{5}$ and $n^{2}$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 12 n \cdot n^{2}}{5}$

Step 1.3.12

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

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Step 1.3.12.1

Move $n^{2}$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 12 (n^{2} n)}{5}$

Step 1.3.12.2

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

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Step 1.3.12.2.1

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

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 12 (n^{2} n^{1})}{5}$

Step 1.3.12.2.2

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

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 12 n^{2 + 1}}{5}$

Step 1.3.12.3

Add $2$ and $1$ .

$n^{5} \cdot 3 + \frac{- 9 n^{4}}{8} + \frac{- 12 n^{3}}{5}$

Step 1.4

Simplify each term.

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Step 1.4.1

Move $3$ to the left of $n^{5}$ .

$3 \cdot n^{5} + \frac{- 9 n^{4}}{8} + \frac{- 12 n^{3}}{5}$

Step 1.4.2

Move the negative in front of the fraction.

$3 n^{5} - \frac{9 n^{4}}{8} + \frac{- 12 n^{3}}{5}$

Step 1.4.3

Move the negative in front of the fraction.

$3 n^{5} - \frac{9 n^{4}}{8} - \frac{12 n^{3}}{5}$

Step 2

The largest exponent is the degree of the polynomial.

$5$