Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

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

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

Step 2

Regroup terms.

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

Step 3

Add parentheses.

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

Step 4

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

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

Step 5

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

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Step 5.1

Move $2 u$ .

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Factor $- 1$ out of $2 u$ .

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

Step 5.5

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

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

Step 5.6

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

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

Step 6

Replace all occurrences of $u$ with $x y$ .

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

Step 7

Remove parentheses.

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

Step 8

Factor.

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Step 8.1

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

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Step 8.1.1

Reorder the expression.

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Step 8.1.1.1

Move $5 y^{2}$ .

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

Step 8.1.1.2

Reorder $- 3$ and $- (x^{2} - 2 x y + 5 y^{2})$ .

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

Step 8.1.2

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 8.1.3

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

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

Step 8.2

Remove unnecessary parentheses.

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

Step 9

Combine exponents.

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Step 9.1

Factor out negative.

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

Step 9.2

Multiply $8$ by $- 1$ .

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

Step 10

Remove unnecessary parentheses.

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