Algebra Examples

$(12 x^{2} - 11 y^{2} - 13 x) - (5 x^{2} - 14 y^{2} - 9 x)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$12 x^{2} - 11 y^{2} - 13 x - (5 x^{2}) - (- 14 y^{2}) - (- 9 x)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$12 x^{2} - 11 y^{2} - 13 x - 5 x^{2} - (- 14 y^{2}) - (- 9 x)$

Step 1.2.2

Multiply $- 14$ by $- 1$ .

$12 x^{2} - 11 y^{2} - 13 x - 5 x^{2} + 14 y^{2} - (- 9 x)$

Step 1.2.3

Multiply $- 9$ by $- 1$ .

$12 x^{2} - 11 y^{2} - 13 x - 5 x^{2} + 14 y^{2} + 9 x$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5 x^{2}$ from $12 x^{2}$ .

$7 x^{2} - 11 y^{2} - 13 x + 14 y^{2} + 9 x$

Step 2.2

Add $- 11 y^{2}$ and $14 y^{2}$ .

$7 x^{2} + 3 y^{2} - 13 x + 9 x$

Step 2.3

Add $- 13 x$ and $9 x$ .

$7 x^{2} + 3 y^{2} - 4 x$