Algebra Examples

$(6 x^{2} - 7 x^{3}) - (2 x^{2} - x^{3})$

Step 1

Remove parentheses.

$6 x^{2} - 7 x^{3} - (2 x^{2} - x^{3})$

Step 2

Factor $- 1$ out of $6 x^{2} - 7 x^{3} - (2 x^{2} - x^{3})$ .

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Step 2.1

Reorder the expression.

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Step 2.1.1

Reorder $2 x^{2}$ and $- x^{3}$ .

$6 x^{2} - 7 x^{3} - (- x^{3} + 2 x^{2})$

Step 2.1.2

Move $6 x^{2}$ .

$- 7 x^{3} - (- x^{3} + 2 x^{2}) + 6 x^{2}$

Step 2.2

Factor $- 1$ out of $- 7 x^{3}$ .

$- (7 x^{3}) - (- x^{3} + 2 x^{2}) + 6 x^{2}$

Step 2.3

Factor $- 1$ out of $6 x^{2}$ .

$- (7 x^{3}) - (- x^{3} + 2 x^{2}) - (- 6 x^{2})$

Step 2.4

Factor $- 1$ out of $- (7 x^{3}) - (- x^{3} + 2 x^{2})$ .

$- (7 x^{3} - x^{3} + 2 x^{2}) - (- 6 x^{2})$

Step 2.5

Factor $- 1$ out of $- (7 x^{3} - x^{3} + 2 x^{2}) - (- 6 x^{2})$ .

$- (7 x^{3} - x^{3} + 2 x^{2} - 6 x^{2})$

Step 3

Subtract $x^{3}$ from $7 x^{3}$ .

$- (6 x^{3} + 2 x^{2} - 6 x^{2})$

Step 4

Subtract $6 x^{2}$ from $2 x^{2}$ .

$- (6 x^{3} - 4 x^{2})$

Step 5

Factor.

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Step 5.1

Factor $2 x^{2}$ out of $6 x^{3} - 4 x^{2}$ .

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Step 5.1.1

Factor $2 x^{2}$ out of $6 x^{3}$ .

$- (2 x^{2} (3 x) - 4 x^{2})$

Step 5.1.2

Factor $2 x^{2}$ out of $- 4 x^{2}$ .

$- (2 x^{2} (3 x) + 2 x^{2} (- 2))$

Step 5.1.3

Factor $2 x^{2}$ out of $2 x^{2} (3 x) + 2 x^{2} (- 2)$ .

$- (2 x^{2} (3 x - 2))$

Step 5.2

Remove unnecessary parentheses.

$- 1 \cdot 2 x^{2} (3 x - 2)$

Step 6

Multiply $- 1$ by $2$ .

$- 2 x^{2} (3 x - 2)$