Algebra Examples

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

Step 1

Expand $(- p + q) (- 1 - q)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $- p \cdot - 1$ .

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Step 2.1.1.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.2

Multiply $p$ by $1$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

Multiply $- 1$ by $- 1$ .

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

Step 2.1.4

Multiply $p$ by $1$ .

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

Step 2.1.5

Move $- 1$ to the left of $q$ .

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

Step 2.1.6

Rewrite $- 1 q$ as $- q$ .

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

Step 2.1.7

Rewrite using the commutative property of multiplication.

$p + p q - q - q \cdot q$

Step 2.1.8

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

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Step 2.1.8.1

Move $q$ .

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

Step 2.1.8.2

Multiply $q$ by $q$ .

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

Step 2.2

Reorder.

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Step 2.2.1

Move $- q$ .

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

Step 2.2.2

Move $p$ .

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