Algebra Examples

$- 4 y^{2} + 3 x y - 12 y + 9 x$

Step 1

Factor out the greatest common factor from each group.

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Step 1.1

Group the first two terms and the last two terms.

$(- 4 y^{2} + 3 x y) - 12 y + 9 x$

Step 1.2

Factor out the greatest common factor (GCF) from each group.

$y (- 4 y + 3 x) + 3 (- 4 y + 3 x)$

Step 2

Factor the polynomial by factoring out the greatest common factor, $- 4 y + 3 x$ .

$(- 4 y + 3 x) (y + 3)$

Step 3

Factor $- 1$ out of $- 4 y + 3 x$ .

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Step 3.1

Reorder $- 4 y$ and $3 x$ .

$(3 x - 4 y) (y + 3)$

Step 3.2

Factor $- 1$ out of $3 x$ .

$(- (- 3 x) - 4 y) (y + 3)$

Step 3.3

Factor $- 1$ out of $- 4 y$ .

$(- (- 3 x) - (4 y)) (y + 3)$

Step 3.4

Factor $- 1$ out of $- (- 3 x) - (4 y)$ .

$- (- 3 x + 4 y) (y + 3)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- 3 x + 4 y$ .

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Step 4.1.1

Factor $- 1$ out of $- 3 x$ .

$- (- (3 x) + 4 y) (y + 3)$

Step 4.1.2

Factor $- 1$ out of $4 y$ .

$- (- (3 x) - (- 4 y)) (y + 3)$

Step 4.1.3

Factor $- 1$ out of $- (3 x) - (- 4 y)$ .

$- - (3 x - 4 y) (y + 3)$

Step 4.2

Remove unnecessary parentheses.

$- - 1 (3 x - 4 y) (y + 3)$

Step 5

Combine exponents.

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Step 5.1

Factor out negative.

$- ((- (3 x - 4 y)) (y + 3))$

Step 5.2

Multiply $- 1$ by $- 1$ .

$1 ((3 x - 4 y) (y + 3))$

Step 5.3

Multiply $3 x - 4 y$ by $1$ .

$(3 x - 4 y) (y + 3)$