Algebra Examples

$- 16 x^{3} y^{2} - 8 x^{2} y - 24 x^{4} y^{4} - 40 x^{2} y^{3}$

Step 1

Factor $8 x^{2} y$ out of $- 16 x^{3} y^{2} - 8 x^{2} y - 24 x^{4} y^{4} - 40 x^{2} y^{3}$ .

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Step 1.1

Factor $8 x^{2} y$ out of $- 16 x^{3} y^{2}$ .

$8 x^{2} y (- 2 x y) - 8 x^{2} y - 24 x^{4} y^{4} - 40 x^{2} y^{3}$

Step 1.2

Factor $8 x^{2} y$ out of $- 8 x^{2} y$ .

$8 x^{2} y (- 2 x y) + 8 x^{2} y (- 1) - 24 x^{4} y^{4} - 40 x^{2} y^{3}$

Step 1.3

Factor $8 x^{2} y$ out of $- 24 x^{4} y^{4}$ .

$8 x^{2} y (- 2 x y) + 8 x^{2} y (- 1) + 8 x^{2} y (- 3 x^{2} y^{3}) - 40 x^{2} y^{3}$

Step 1.4

Factor $8 x^{2} y$ out of $- 40 x^{2} y^{3}$ .

$8 x^{2} y (- 2 x y) + 8 x^{2} y (- 1) + 8 x^{2} y (- 3 x^{2} y^{3}) + 8 x^{2} y (- 5 y^{2})$

Step 1.5

Factor $8 x^{2} y$ out of $8 x^{2} y (- 2 x y) + 8 x^{2} y (- 1)$ .

$8 x^{2} y (- 2 x y - 1) + 8 x^{2} y (- 3 x^{2} y^{3}) + 8 x^{2} y (- 5 y^{2})$

Step 1.6

Factor $8 x^{2} y$ out of $8 x^{2} y (- 2 x y - 1) + 8 x^{2} y (- 3 x^{2} y^{3})$ .

$8 x^{2} y (- 2 x y - 1 - 3 x^{2} y^{3}) + 8 x^{2} y (- 5 y^{2})$

Step 1.7

Factor $8 x^{2} y$ out of $8 x^{2} y (- 2 x y - 1 - 3 x^{2} y^{3}) + 8 x^{2} y (- 5 y^{2})$ .

$8 x^{2} y (- 2 x y - 1 - 3 x^{2} y^{3} - 5 y^{2})$

Step 2

Factor.

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Step 2.1

Factor $- 1$ out of $- 2 x y - 1 - 3 x^{2} y^{3} - 5 y^{2}$ .

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Step 2.1.1

Reorder the expression.

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Step 2.1.1.1

Move $- 1$ .

$8 x^{2} y (- 2 x y - 3 x^{2} y^{3} - 5 y^{2} - 1)$

Step 2.1.1.2

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

$8 x^{2} y (- 3 x^{2} y^{3} - 2 x y - 5 y^{2} - 1)$

Step 2.1.2

Factor $- 1$ out of $- 3 x^{2} y^{3}$ .

$8 x^{2} y (- (3 x^{2} y^{3}) - 2 x y - 5 y^{2} - 1)$

Step 2.1.3

Factor $- 1$ out of $- 2 x y$ .

$8 x^{2} y (- (3 x^{2} y^{3}) - (2 x y) - 5 y^{2} - 1)$

Step 2.1.4

Factor $- 1$ out of $- 5 y^{2}$ .

$8 x^{2} y (- (3 x^{2} y^{3}) - (2 x y) - (5 y^{2}) - 1)$

Step 2.1.5

Rewrite $- 1$ as $- 1 (1)$ .

$8 x^{2} y (- (3 x^{2} y^{3}) - (2 x y) - (5 y^{2}) - 1 (1))$

Step 2.1.6

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

$8 x^{2} y (- (3 x^{2} y^{3} + 2 x y) - (5 y^{2}) - 1 (1))$

Step 2.1.7

Factor $- 1$ out of $- (3 x^{2} y^{3} + 2 x y) - (5 y^{2})$ .

$8 x^{2} y (- (3 x^{2} y^{3} + 2 x y + 5 y^{2}) - 1 (1))$

Step 2.1.8

Factor $- 1$ out of $- (3 x^{2} y^{3} + 2 x y + 5 y^{2}) - 1 (1)$ .

$8 x^{2} y (- (3 x^{2} y^{3} + 2 x y + 5 y^{2} + 1))$

Step 2.2

Remove unnecessary parentheses.

$8 x^{2} y \cdot - 1 (3 x^{2} y^{3} + 2 x y + 5 y^{2} + 1)$

Step 3

Combine exponents.

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Step 3.1

Factor out negative.

$- (8 x^{2} y (3 x^{2} y^{3} + 2 x y + 5 y^{2} + 1))$

Step 3.2

Multiply $8$ by $- 1$ .

$- 8 (x^{2} y (3 x^{2} y^{3} + 2 x y + 5 y^{2} + 1))$

Step 4

Remove unnecessary parentheses.

$- 8 x^{2} y (3 x^{2} y^{3} + 2 x y + 5 y^{2} + 1)$