Algebra Examples

$(7 x - 12 x^{4} y^{4}) + (- 11 x^{3} y^{2} + 6 x - x^{4} y^{4}) - (7 x^{4} y^{4} - 12 x^{3} y^{2})$

Step 1

Remove parentheses.

$7 x - 12 x^{4} y^{4} - 11 x^{3} y^{2} + 6 x - x^{4} y^{4} - (7 x^{4} y^{4} - 12 x^{3} y^{2})$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$7 x - 12 x^{4} y^{4} - 11 x^{3} y^{2} + 6 x - x^{4} y^{4} - (7 x^{4} y^{4}) - (- 12 x^{3} y^{2})$

Step 2.2

Multiply $7$ by $- 1$ .

$7 x - 12 x^{4} y^{4} - 11 x^{3} y^{2} + 6 x - x^{4} y^{4} - 7 (x^{4} y^{4}) - (- 12 x^{3} y^{2})$

Step 2.3

Multiply $- 12$ by $- 1$ .

$7 x - 12 x^{4} y^{4} - 11 x^{3} y^{2} + 6 x - x^{4} y^{4} - 7 (x^{4} y^{4}) + 12 (x^{3} y^{2})$

Step 2.4

Remove parentheses.

$7 x - 12 x^{4} y^{4} - 11 x^{3} y^{2} + 6 x - x^{4} y^{4} - 7 x^{4} y^{4} + 12 x^{3} y^{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $7 x$ and $6 x$ .

$- 12 x^{4} y^{4} - 11 x^{3} y^{2} + 13 x - x^{4} y^{4} - 7 x^{4} y^{4} + 12 x^{3} y^{2}$

Step 3.2

Subtract $x^{4} y^{4}$ from $- 12 x^{4} y^{4}$ .

$- 13 x^{4} y^{4} - 11 x^{3} y^{2} + 13 x - 7 x^{4} y^{4} + 12 x^{3} y^{2}$

Step 3.3

Subtract $7 x^{4} y^{4}$ from $- 13 x^{4} y^{4}$ .

$- 20 x^{4} y^{4} - 11 x^{3} y^{2} + 13 x + 12 x^{3} y^{2}$

Step 3.4

Add $- 11 x^{3} y^{2}$ and $12 x^{3} y^{2}$ .

$- 20 x^{4} y^{4} + 1 x^{3} y^{2} + 13 x$

Step 3.5

Multiply $x^{3}$ by $1$ .

$- 20 x^{4} y^{4} + x^{3} y^{2} + 13 x$