Finite Math Examples

$p (p - q) - q (q - p)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$p \cdot p + p (- q) - q (q - p)$

Step 1.2

Multiply $p$ by $p$ .

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Apply the distributive property.

$p^{2} - p q - q \cdot q - q (- p)$

Step 1.5

Multiply $q$ by $q$ by adding the exponents.

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Step 1.5.1

Move $q$ .

$p^{2} - p q - (q \cdot q) - q (- p)$

Step 1.5.2

Multiply $q$ by $q$ .

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

Step 1.6

Rewrite using the commutative property of multiplication.

$p^{2} - p q - q^{2} - 1 \cdot - 1 q p$

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$p^{2} - p q - q^{2} + 1 q p$

Step 1.7.2

Multiply $q$ by $1$ .

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

Step 2

Combine the opposite terms in $p^{2} - p q - q^{2} + q p$ .

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Step 2.1

Reorder the factors in the terms $- p q$ and $q p$ .

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

Step 2.2

Add $- p q$ and $p q$ .

$p^{2} - q^{2} + 0$

Step 2.3

Add $p^{2} - q^{2}$ and $0$ .

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