Finite Math Examples

$p^{2} + 2 p q - 24 p^{2}$

Step 1

Subtract $24 p^{2}$ from $p^{2}$ .

$- 23 p^{2} + 2 p q$

Step 2

Factor $- p$ out of $- 23 p^{2} + 2 p q$ .

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Step 2.1

Reorder $- 23 p^{2}$ and $2 p q$ .

$2 p q - 23 p^{2}$

Step 2.2

Factor $- p$ out of $2 p q$ .

$- p (- 2 q) - 23 p^{2}$

Step 2.3

Factor $- p$ out of $- 23 p^{2}$ .

$- p (- 2 q) - p (23 p)$

Step 2.4

Factor $- p$ out of $- p (- 2 q) - p (23 p)$ .

$- p (- 2 q + 23 p)$

$- p (- 2 q + 23 p)$

Step 3

Factor.

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Step 3.1

Factor $- 1$ out of $- 2 q + 23 p$ .

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Step 3.1.1

Reorder $- 2 q$ and $23 p$ .

$- p (23 p - 2 q)$

Step 3.1.2

Factor $- 1$ out of $23 p$ .

$- p (- (- 23 p) - 2 q)$

Step 3.1.3

Factor $- 1$ out of $- 2 q$ .

$- p (- (- 23 p) - (2 q))$

Step 3.1.4

Factor $- 1$ out of $- (- 23 p) - (2 q)$ .

$- p (- (- 23 p + 2 q))$

$- p (- (- 23 p + 2 q))$

Step 3.2

Remove unnecessary parentheses.

$- p \cdot - 1 (- 23 p + 2 q)$

$- p \cdot - 1 (- 23 p + 2 q)$

Step 4

Combine exponents.

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Step 4.1

Factor out negative.

$- (p \cdot - 1 (- 23 p + 2 q))$

Step 4.2

Multiply $- 1$ by $- 1$ .

$1 (p (- 23 p + 2 q))$

Step 4.3

Multiply $p$ by $1$ .

$p (- 23 p + 2 q)$

$p (- 23 p + 2 q)$

Step 5

Factor.

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Step 5.1

Factor $- 1$ out of $- 23 p + 2 q$ .

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Step 5.1.1

Factor $- 1$ out of $- 23 p$ .

$p (- (23 p) + 2 q)$

Step 5.1.2

Factor $- 1$ out of $2 q$ .

$p (- (23 p) - (- 2 q))$

Step 5.1.3

Factor $- 1$ out of $- (23 p) - (- 2 q)$ .

$p (- (23 p - 2 q))$

$p (- (23 p - 2 q))$

Step 5.2

Remove unnecessary parentheses.

$p \cdot - 1 (23 p - 2 q)$

$p \cdot - 1 (23 p - 2 q)$

Step 6

Factor out negative.

$- (p (23 p - 2 q))$

Step 7

Remove unnecessary parentheses.

$- p (23 p - 2 q)$

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