Algebra Examples

$(13 x^{3} - 13 x^{4}) + (6 x y^{3} - 9 x^{3}) - (x^{4} + 12 x y^{3})$

Step 1

Remove parentheses.

$13 x^{3} - 13 x^{4} + 6 x y^{3} - 9 x^{3} - (x^{4} + 12 x y^{3})$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$13 x^{3} - 13 x^{4} + 6 x y^{3} - 9 x^{3} - x^{4} - (12 x y^{3})$

Step 2.2

Multiply $12$ by $- 1$ .

$13 x^{3} - 13 x^{4} + 6 x y^{3} - 9 x^{3} - x^{4} - 12 x y^{3}$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $9 x^{3}$ from $13 x^{3}$ .

$4 x^{3} - 13 x^{4} + 6 x y^{3} - x^{4} - 12 x y^{3}$

Step 3.2

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

$4 x^{3} - 14 x^{4} + 6 x y^{3} - 12 x y^{3}$

Step 3.3

Subtract $12 x y^{3}$ from $6 x y^{3}$ .

$4 x^{3} - 14 x^{4} - 6 x y^{3}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Move $4 x^{3}$ .

$- 14 x^{4} - 6 x y^{3} + 4 x^{3}$

Step 3.4.2

Reorder $- 14 x^{4}$ and $- 6 x y^{3}$ .

$- 6 x y^{3} - 14 x^{4} + 4 x^{3}$