Basic Math Examples

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

Step 1

Apply the distributive property.

$(2 p + 2 \cdot - 2) (r - 2) + 2 (q - 2) (r - 2) + p q$

Step 2

Multiply $2$ by $- 2$ .

$(2 p - 4) (r - 2) + 2 (q - 2) (r - 2) + p q$

Step 3

Expand $(2 p - 4) (r - 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$2 p (r - 2) - 4 (r - 2) + 2 (q - 2) (r - 2) + p q$

Step 3.2

Apply the distributive property.

$2 p r + 2 p \cdot - 2 - 4 (r - 2) + 2 (q - 2) (r - 2) + p q$

Step 3.3

Apply the distributive property.

$2 p r + 2 p \cdot - 2 - 4 r - 4 \cdot - 2 + 2 (q - 2) (r - 2) + p q$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 2$ by $2$ .

$2 p r - 4 p - 4 r - 4 \cdot - 2 + 2 (q - 2) (r - 2) + p q$

Step 4.2

Multiply $- 4$ by $- 2$ .

$2 p r - 4 p - 4 r + 8 + 2 (q - 2) (r - 2) + p q$

Step 5

Apply the distributive property.

$2 p r - 4 p - 4 r + 8 + (2 q + 2 \cdot - 2) (r - 2) + p q$

Step 6

Multiply $2$ by $- 2$ .

$2 p r - 4 p - 4 r + 8 + (2 q - 4) (r - 2) + p q$

Step 7

Expand $(2 q - 4) (r - 2)$ using the FOIL Method.

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Step 7.1

Apply the distributive property.

$2 p r - 4 p - 4 r + 8 + 2 q (r - 2) - 4 (r - 2) + p q$

Step 7.2

Apply the distributive property.

$2 p r - 4 p - 4 r + 8 + 2 q r + 2 q \cdot - 2 - 4 (r - 2) + p q$

Step 7.3

Apply the distributive property.

$2 p r - 4 p - 4 r + 8 + 2 q r + 2 q \cdot - 2 - 4 r - 4 \cdot - 2 + p q$

Step 8

Simplify each term.

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Step 8.1

Multiply $- 2$ by $2$ .

$2 p r - 4 p - 4 r + 8 + 2 q r - 4 q - 4 r - 4 \cdot - 2 + p q$

Step 8.2

Multiply $- 4$ by $- 2$ .

$2 p r - 4 p - 4 r + 8 + 2 q r - 4 q - 4 r + 8 + p q$

Step 9

Subtract $4 r$ from $- 4 r$ .

$2 p r - 4 p + 8 + 2 q r - 4 q - 8 r + 8 + p q$

Step 10

Add $8$ and $8$ .

$2 p r - 4 p + 2 q r - 4 q - 8 r + 16 + p q$