Finite Math Examples

$((2 m) i - 2 m j) \cdot ((4 m) i + (2 m) j)$

Step 1

Multiply $2 m$ by $i$ .

$(2 m i - 2 m j) \cdot ((4 m) i + (2 m) j)$

Step 2

Factor $2 m$ out of $2 m i - 2 m j$ .

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Step 2.1

Factor $2 m$ out of $2 m i$ .

$(2 m (i) - 2 m j) \cdot ((4 m) i + (2 m) j)$

Step 2.2

Factor $2 m$ out of $- 2 m j$ .

$(2 m (i) + 2 m (- 1 j)) \cdot ((4 m) i + (2 m) j)$

Step 2.3

Factor $2 m$ out of $2 m (i) + 2 m (- 1 j)$ .

$2 m (i - 1 j) \cdot ((4 m) i + (2 m) j)$

$2 m (i - 1 j) \cdot ((4 m) i + (2 m) j)$

Step 3

Rewrite $- 1 j$ as $- j$ .

$2 m (i - j) \cdot ((4 m) i + (2 m) j)$

Step 4

Multiply $4 m$ by $i$ .

$2 m (i - j) \cdot (4 m i + (2 m) j)$

Step 5

Multiply $2 m$ by $j$ .

$2 m (i - j) \cdot (4 m i + 2 m j)$

Step 6

Factor.

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Step 6.1

Factor $2 m$ out of $4 m i + 2 m j$ .

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Step 6.1.1

Factor $2 m$ out of $4 m i$ .

$2 m (i - j) \cdot (2 m (2 i) + 2 m j)$

Step 6.1.2

Factor $2 m$ out of $2 m j$ .

$2 m (i - j) \cdot (2 m (2 i) + 2 m (j))$

Step 6.1.3

Factor $2 m$ out of $2 m (2 i) + 2 m (j)$ .

$2 m (i - j) \cdot (2 m (2 i + j))$

$2 m (i - j) \cdot (2 m (2 i + j))$

Step 6.2

Remove unnecessary parentheses.

$2 m (i - j) \cdot 2 m (2 i + j)$

$2 m (i - j) \cdot 2 m (2 i + j)$

Step 7

Combine exponents.

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Step 7.1

Multiply $2$ by $2$ .

$4 m (i - j) m (2 i + j)$

Step 7.2

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

$4 (m^{1} m) (i - j) (2 i + j)$

Step 7.3

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

$4 (m^{1} m^{1}) (i - j) (2 i + j)$

Step 7.4

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

$4 m^{1 + 1} (i - j) (2 i + j)$

Step 7.5

Add $1$ and $1$ .

$4 m^{2} (i - j) (2 i + j)$

$4 m^{2} (i - j) (2 i + j)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$