Basic Math Examples

$(18 x + 13 x y - 11 y) - (21 x - 14 x y - 5 y)$

Step 1

Regroup terms.

$18 x + 13 x y - 11 y - (21 x - 14 x y - 5 y)$

Step 2

Apply the distributive property.

$18 x + 13 x y - 11 y - (21 x) - (- 14 x y) - (- 5 y)$

Step 3

Simplify.

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Step 3.1

Multiply $21$ by $- 1$ .

$18 x + 13 x y - 11 y - 21 x - (- 14 x y) - (- 5 y)$

Step 3.2

Multiply $- 14$ by $- 1$ .

$18 x + 13 x y - 11 y - 21 x + 14 (x y) - (- 5 y)$

Step 3.3

Multiply $- 5$ by $- 1$ .

$18 x + 13 x y - 11 y - 21 x + 14 (x y) + 5 y$

Step 4

Remove parentheses.

$18 x + 13 x y - 11 y - 21 x + 14 x y + 5 y$

Step 5

Add $13 x y$ and $14 x y$ .

$18 x + 27 x y - 11 y - 21 x + 5 y$

Step 6

Add $- 11 y$ and $5 y$ .

$18 x + 27 x y - 21 x - 6 y$

Step 7

Factor $3$ out of $27 x y - 21 x - 6 y$ .

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Step 7.1

Factor $3$ out of $27 x y$ .

$18 x + 3 (9 x y) - 21 x - 6 y$

Step 7.2

Factor $3$ out of $- 21 x$ .

$18 x + 3 (9 x y) + 3 (- 7 x) - 6 y$

Step 7.3

Factor $3$ out of $- 6 y$ .

$18 x + 3 (9 x y) + 3 (- 7 x) + 3 (- 2 y)$

Step 7.4

Factor $3$ out of $3 (9 x y) + 3 (- 7 x)$ .

$18 x + 3 (9 x y - 7 x) + 3 (- 2 y)$

Step 7.5

Factor $3$ out of $3 (9 x y - 7 x) + 3 (- 2 y)$ .

$18 x + 3 (9 x y - 7 x - 2 y)$

Step 8

Factor $3$ out of $18 x + 3 (9 x y - 7 x - 2 y)$ .

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Step 8.1

Factor $3$ out of $18 x$ .

$3 (6 x) + 3 (9 x y - 7 x - 2 y)$

Step 8.2

Factor $3$ out of $3 (6 x) + 3 (9 x y - 7 x - 2 y)$ .

$3 (6 x + 9 x y - 7 x - 2 y)$

Step 9

Subtract $7 x$ from $6 x$ .

$3 (9 x y - x - 2 y)$