Basic Math Examples

$(7 m^{3} + 14 m^{2} - 21 m) \div 7 m$

Step 1

Rewrite the division as a fraction.

$\frac{7 m^{3} + 14 m^{2} - 21 m}{7 m}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $7 m$ out of $7 m^{3} + 14 m^{2} - 21 m$ .

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Step 2.1.1

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

$\frac{7 m (m^{2}) + 14 m^{2} - 21 m}{7 m}$

Step 2.1.2

Factor $7 m$ out of $14 m^{2}$ .

$\frac{7 m (m^{2}) + 7 m (2 m) - 21 m}{7 m}$

Step 2.1.3

Factor $7 m$ out of $- 21 m$ .

$\frac{7 m (m^{2}) + 7 m (2 m) + 7 m (- 3)}{7 m}$

Step 2.1.4

Factor $7 m$ out of $7 m (m^{2}) + 7 m (2 m)$ .

$\frac{7 m (m^{2} + 2 m) + 7 m (- 3)}{7 m}$

Step 2.1.5

Factor $7 m$ out of $7 m (m^{2} + 2 m) + 7 m (- 3)$ .

$\frac{7 m (m^{2} + 2 m - 3)}{7 m}$

Step 2.2

Factor $m^{2} + 2 m - 3$ using the AC method.

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Step 2.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $2$ .

$- 1, 3$

Step 2.2.2

Write the factored form using these integers.

$\frac{7 m ((m - 1) (m + 3))}{7 m}$

$\frac{7 m (m - 1) (m + 3)}{7 m}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $7$ .

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Step 3.1.1

Cancel the common factor.

$\frac{7 m (m - 1) (m + 3)}{7 m}$

Step 3.1.2

Rewrite the expression.

$\frac{(m (m - 1)) (m + 3)}{m}$

Step 3.2

Cancel the common factor of $m$ .

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Step 3.2.1

Cancel the common factor.

$\frac{m (m - 1) (m + 3)}{m}$

Step 3.2.2

Divide $(m - 1) (m + 3)$ by $1$ .

$(m - 1) (m + 3)$

Step 4

Expand $(m - 1) (m + 3)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$m (m + 3) - 1 (m + 3)$

Step 4.2

Apply the distributive property.

$m \cdot m + m \cdot 3 - 1 (m + 3)$

Step 4.3

Apply the distributive property.

$m \cdot m + m \cdot 3 - 1 m - 1 \cdot 3$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Multiply $m$ by $m$ .

$m^{2} + m \cdot 3 - 1 m - 1 \cdot 3$

Step 5.1.2

Move $3$ to the left of $m$ .

$m^{2} + 3 \cdot m - 1 m - 1 \cdot 3$

Step 5.1.3

Rewrite $- 1 m$ as $- m$ .

$m^{2} + 3 m - m - 1 \cdot 3$

Step 5.1.4

Multiply $- 1$ by $3$ .

$m^{2} + 3 m - m - 3$

Step 5.2

Subtract $m$ from $3 m$ .

$m^{2} + 2 m - 3$