Calculus Examples

$(3 p (14) + \frac{p {(14)}^{2}}{2}) - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1

Simplify each term.

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Step 1.1

Multiply $14$ by $3$ .

$42 p + \frac{p {(14)}^{2}}{2} - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.2

Raise $14$ to the power of $2$ .

$42 p + \frac{p \cdot 196}{2} - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.3

Cancel the common factor of $196$ and $2$ .

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Step 1.3.1

Factor $2$ out of $p \cdot 196$ .

$42 p + \frac{2 (p \cdot 98)}{2} - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $2$ .

$42 p + \frac{2 (p \cdot 98)}{2 (1)} - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.3.2.2

Cancel the common factor.

$42 p + \frac{2 (p \cdot 98)}{2 \cdot 1} - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.3.2.3

Rewrite the expression.

$42 p + \frac{p \cdot 98}{1} - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.3.2.4

Divide $p \cdot 98$ by $1$ .

$42 p + p \cdot 98 - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.4

Move $98$ to the left of $p$ .

$42 p + 98 \cdot p - (3 p (2) + \frac{p {(2)}^{2}}{2})$

Step 1.5

Simplify each term.

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Step 1.5.1

Multiply $2$ by $3$ .

$42 p + 98 p - (6 p + \frac{p {(2)}^{2}}{2})$

Step 1.5.2

Cancel the common factor of ${(2)}^{2}$ and $2$ .

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Step 1.5.2.1

Factor $2$ out of $p {(2)}^{2}$ .

$42 p + 98 p - (6 p + \frac{2 (p \cdot 2)}{2})$

Step 1.5.2.2

Cancel the common factors.

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Step 1.5.2.2.1

Factor $2$ out of $2$ .

$42 p + 98 p - (6 p + \frac{2 (p \cdot 2)}{2 (1)})$

Step 1.5.2.2.2

Cancel the common factor.

$42 p + 98 p - (6 p + \frac{2 (p \cdot 2)}{2 \cdot 1})$

Step 1.5.2.2.3

Rewrite the expression.

$42 p + 98 p - (6 p + \frac{p \cdot 2}{1})$

Step 1.5.2.2.4

Divide $p \cdot 2$ by $1$ .

$42 p + 98 p - (6 p + p \cdot 2)$

Step 1.5.3

Move $2$ to the left of $p$ .

$42 p + 98 p - (6 p + 2 p)$

Step 1.6

Add $6 p$ and $2 p$ .

$42 p + 98 p - (8 p)$

Step 1.7

Multiply $8$ by $- 1$ .

$42 p + 98 p - 8 p$

Step 2

Simplify by adding terms.

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Step 2.1

Add $42 p$ and $98 p$ .

$140 p - 8 p$

Step 2.2

Subtract $8 p$ from $140 p$ .

$132 p$