Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

$a p - a q + q - p$

Step 2

Reorder terms.

$a p - a q - p + q$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

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

Step 3.2

Factor out the greatest common factor (GCF) from each group.

$a (p - 1 q) - (p - q)$

Step 4

Factor the polynomial by factoring out the greatest common factor, $p - 1 q$ .

$(p - 1 q) (a - 1)$

Step 5

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

$(p - q) (a - 1)$