Algebra Examples

$2 p (q - 8) + 5 w (8 - q)$

Step 1

Apply the distributive property.

$2 p q + 2 p \cdot - 8 + 5 w (8 - q)$

Step 2

Multiply $- 8$ by $2$ .

$2 p q - 16 p + 5 w (8 - q)$

Step 3

Apply the distributive property.

$2 p q - 16 p + 5 w \cdot 8 + 5 w (- q)$

Step 4

Multiply $8$ by $5$ .

$2 p q - 16 p + 40 w + 5 w (- q)$

Step 5

Rewrite using the commutative property of multiplication.

$2 p q - 16 p + 40 w + 5 \cdot - 1 w q$

Step 6

Multiply $5$ by $- 1$ .

$2 p q - 16 p + 40 w - 5 w q$

Step 7

Rewrite $2 p q - 16 p + 40 w - 5 w q$ in a factored form.

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Step 7.1

Reorder terms.

$2 p q - 5 q w - 16 p + 40 w$

Step 7.2

Factor out the greatest common factor from each group.

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Step 7.2.1

Group the first two terms and the last two terms.

$(2 p q - 5 q w) - 16 p + 40 w$

Step 7.2.2

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

$q (2 p - 5 w) - 8 (2 p - 5 w)$

Step 7.3

Factor the polynomial by factoring out the greatest common factor, $2 p - 5 w$ .

$(2 p - 5 w) (q - 8)$