Algebra Examples

$7 x^{5} y^{4} - 9 x^{3} y - 2 x y^{3}$

Step 1

Factor $x y$ out of $7 x^{5} y^{4} - 9 x^{3} y - 2 x y^{3}$ .

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Step 1.1

Factor $x y$ out of $7 x^{5} y^{4}$ .

$x y (7 x^{4} y^{3}) - 9 x^{3} y - 2 x y^{3}$

Step 1.2

Factor $x y$ out of $- 9 x^{3} y$ .

$x y (7 x^{4} y^{3}) + x y (- 9 x^{2}) - 2 x y^{3}$

Step 1.3

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

$x y (7 x^{4} y^{3}) + x y (- 9 x^{2}) + x y (- 2 y^{2})$

Step 1.4

Factor $x y$ out of $x y (7 x^{4} y^{3}) + x y (- 9 x^{2})$ .

$x y (7 x^{4} y^{3} - 9 x^{2}) + x y (- 2 y^{2})$

Step 1.5

Factor $x y$ out of $x y (7 x^{4} y^{3} - 9 x^{2}) + x y (- 2 y^{2})$ .

$x y (7 x^{4} y^{3} - 9 x^{2} - 2 y^{2})$

Step 2

Add parentheses.

$x y (7 (x^{4} y^{3}) - 9 x^{2} - 2 y^{2})$

Step 3

Let $u = x^{4} y^{3}$ . Substitute $u$ for all occurrences of $x^{4} y^{3}$ .

$x y (7 u - 9 x^{2} - 2 y^{2})$

Step 4

Factor $- 1$ out of $7 u - 9 x^{2} - 2 y^{2}$ .

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Step 4.1

Move $7 u$ .

$x y (- 9 x^{2} - 2 y^{2} + 7 u)$

Step 4.2

Factor $- 1$ out of $- 9 x^{2}$ .

$x y (- (9 x^{2}) - 2 y^{2} + 7 u)$

Step 4.3

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

$x y (- (9 x^{2}) - (2 y^{2}) + 7 u)$

Step 4.4

Factor $- 1$ out of $7 u$ .

$x y (- (9 x^{2}) - (2 y^{2}) - (- 7 u))$

Step 4.5

Factor $- 1$ out of $- (9 x^{2}) - (2 y^{2})$ .

$x y (- (9 x^{2} + 2 y^{2}) - (- 7 u))$

Step 4.6

Factor $- 1$ out of $- (9 x^{2} + 2 y^{2}) - (- 7 u)$ .

$x y (- (9 x^{2} + 2 y^{2} - 7 u))$

Step 5

Replace all occurrences of $u$ with $x^{4} y^{3}$ .

$x y (- (9 x^{2} + 2 y^{2} - 7 (x^{4} y^{3})))$

Step 6

Factor.

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Step 6.1

Remove parentheses.

$x y (- (9 x^{2} + 2 y^{2} - 7 x^{4} y^{3}))$

Step 6.2

Remove unnecessary parentheses.

$x y \cdot - 1 (9 x^{2} + 2 y^{2} - 7 x^{4} y^{3})$

Step 7

Factor out negative.

$- (x y (9 x^{2} + 2 y^{2} - 7 x^{4} y^{3}))$

Step 8

Remove unnecessary parentheses.

$- x y (9 x^{2} + 2 y^{2} - 7 x^{4} y^{3})$

Step 9

Factor.

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Step 9.1

Factor $- 1$ out of $9 x^{2} + 2 y^{2} - 7 x^{4} y^{3}$ .

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Step 9.1.1

Reorder the expression.

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Step 9.1.1.1

Move $9 x^{2}$ .

$- x y (2 y^{2} - 7 x^{4} y^{3} + 9 x^{2})$

Step 9.1.1.2

Reorder $2 y^{2}$ and $- 7 x^{4} y^{3}$ .

$- x y (- 7 x^{4} y^{3} + 2 y^{2} + 9 x^{2})$

Step 9.1.2

Factor $- 1$ out of $- 7 x^{4} y^{3}$ .

$- x y (- (7 x^{4} y^{3}) + 2 y^{2} + 9 x^{2})$

Step 9.1.3

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

$- x y (- (7 x^{4} y^{3}) - (- 2 y^{2}) + 9 x^{2})$

Step 9.1.4

Factor $- 1$ out of $9 x^{2}$ .

$- x y (- (7 x^{4} y^{3}) - (- 2 y^{2}) - (- 9 x^{2}))$

Step 9.1.5

Factor $- 1$ out of $- (7 x^{4} y^{3}) - (- 2 y^{2})$ .

$- x y (- (7 x^{4} y^{3} - 2 y^{2}) - (- 9 x^{2}))$

Step 9.1.6

Factor $- 1$ out of $- (7 x^{4} y^{3} - 2 y^{2}) - (- 9 x^{2})$ .

$- x y (- (7 x^{4} y^{3} - 2 y^{2} - 9 x^{2}))$

Step 9.2

Remove unnecessary parentheses.

$- x y \cdot - 1 (7 x^{4} y^{3} - 2 y^{2} - 9 x^{2})$

Step 10

Combine exponents.

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Step 10.1

Factor out negative.

$- (x y \cdot - 1 (7 x^{4} y^{3} - 2 y^{2} - 9 x^{2}))$

Step 10.2

Multiply $- 1$ by $- 1$ .

$1 (x y (7 x^{4} y^{3} - 2 y^{2} - 9 x^{2}))$

Step 10.3

Multiply $x$ by $1$ .

$x (y (7 x^{4} y^{3} - 2 y^{2} - 9 x^{2}))$

Step 11

Remove unnecessary parentheses.

$x y (7 x^{4} y^{3} - 2 y^{2} - 9 x^{2})$