Factor gx^2-3hx^2-6fy^2-gy^2+6fx^2+3hy^2

$g x^{2} - 3 h x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2} + 3 h y^{2}$

Regroup terms.

$- 3 h x^{2} + 3 h y^{2} + g x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2}$

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

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

$- 3 h (x^{2}) + 3 h y^{2} + g x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2}$

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

$- 3 h (x^{2}) - 3 h (- 1 y^{2}) + g x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2}$

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

$- 3 h (x^{2} - 1 y^{2}) + g x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2}$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$- 3 h ((x + y) (x - y)) + g x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2}$

Remove unnecessary parentheses.

$- 3 h (x + y) (x - y) + g x^{2} - 6 f y^{2} - g y^{2} + 6 f x^{2}$

Regroup terms.

$- 3 h (x + y) (x - y) + g x^{2} - g y^{2} - 6 f y^{2} + 6 f x^{2}$

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

Factor $g$ out of $g x^{2}$ .

$- 3 h (x + y) (x - y) + g (x^{2}) - g y^{2} - 6 f y^{2} + 6 f x^{2}$

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

$- 3 h (x + y) (x - y) + g (x^{2}) + g (- 1 y^{2}) - 6 f y^{2} + 6 f x^{2}$

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

$- 3 h (x + y) (x - y) + g (x^{2} - 1 y^{2}) - 6 f y^{2} + 6 f x^{2}$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$- 3 h (x + y) (x - y) + g ((x + y) (x - y)) - 6 f y^{2} + 6 f x^{2}$

Remove unnecessary parentheses.

$- 3 h (x + y) (x - y) + g (x + y) (x - y) - 6 f y^{2} + 6 f x^{2}$

Factor $6 f$ out of $- 6 f y^{2} + 6 f x^{2}$ .

Factor $6 f$ out of $- 6 f y^{2}$ .

$- 3 h (x + y) (x - y) + g (x + y) (x - y) + 6 f (- 1 y^{2}) + 6 f x^{2}$

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

$- 3 h (x + y) (x - y) + g (x + y) (x - y) + 6 f (- 1 y^{2}) + 6 f (x^{2})$

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

$- 3 h (x + y) (x - y) + g (x + y) (x - y) + 6 f (- 1 y^{2} + x^{2})$

Reorder $- 1 y^{2}$ and $x^{2}$ .

$- 3 h (x + y) (x - y) + g (x + y) (x - y) + 6 f (x^{2} - 1 y^{2})$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$- 3 h (x + y) (x - y) + g (x + y) (x - y) + 6 f ((x + y) (x - y))$

Remove unnecessary parentheses.

$- 3 h (x + y) (x - y) + g (x + y) (x - y) + 6 f (x + y) (x - y)$

Factor $(x + y) (x - y)$ out of $g (x + y) (x - y) + 6 f (x + y) (x - y)$ .

Factor $(x + y) (x - y)$ out of $g (x + y) (x - y)$ .

$- 3 h (x + y) (x - y) + (x + y) (x - y) (g) + 6 f (x + y) (x - y)$

Factor $(x + y) (x - y)$ out of $6 f (x + y) (x - y)$ .

$- 3 h (x + y) (x - y) + (x + y) (x - y) (g) + (x + y) (x - y) (6 f)$

Factor $(x + y) (x - y)$ out of $(x + y) (x - y) (g) + (x + y) (x - y) (6 f)$ .

$- 3 h (x + y) (x - y) + (x + y) (x - y) (g + 6 f)$

Factor $(x + y) (x - y)$ out of $- 3 h (x + y) (x - y) + (x + y) (x - y) (g + 6 f)$ .

Factor $(x + y) (x - y)$ out of $- 3 h (x + y) (x - y)$ .

$(x + y) (x - y) (- 3 h) + (x + y) (x - y) (g + 6 f)$

Factor $(x + y) (x - y)$ out of $(x + y) (x - y) (- 3 h) + (x + y) (x - y) (g + 6 f)$ .

$(x + y) (x - y) (- 3 h + g + 6 f)$

Factor.

Factor $- 1$ out of $- 3 h + g + 6 f$ .

Reorder the expression.

Move $- 3 h$ .

$(x + y) (x - y) (g + 6 f - 3 h)$

Reorder $g$ and $6 f$ .

$(x + y) (x - y) (6 f + g - 3 h)$

Factor $- 1$ out of $6 f$ .

$(x + y) (x - y) (- (- 6 f) + g - 3 h)$

Factor $- 1$ out of $g$ .

$(x + y) (x - y) (- (- 6 f) - 1 (- g) - 3 h)$

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

$(x + y) (x - y) (- (- 6 f) - 1 (- g) - (3 h))$

Factor $- 1$ out of $- (- 6 f) - 1 (- g)$ .

$(x + y) (x - y) (- (- 6 f - g) - (3 h))$

Factor $- 1$ out of $- (- 6 f - g) - (3 h)$ .

$(x + y) (x - y) (- (- 6 f - g + 3 h))$

Remove unnecessary parentheses.

$(x + y) (x - y) \cdot - 1 (- 6 f - g + 3 h)$

Factor out negative.

$- ((x + y) (x - y) (- 6 f - g + 3 h))$

Remove unnecessary parentheses.

$- (x + y) (x - y) (- 6 f - g + 3 h)$

Factor.

Factor $- 1$ out of $- 6 f - g + 3 h$ .

Factor $- 1$ out of $- 6 f$ .

$- (x + y) (x - y) (- (6 f) - g + 3 h)$

Factor $- 1$ out of $- g$ .

$- (x + y) (x - y) (- (6 f) - (g) + 3 h)$

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

$- (x + y) (x - y) (- (6 f) - (g) - (- 3 h))$

Factor $- 1$ out of $- (6 f) - (g)$ .

$- (x + y) (x - y) (- (6 f + g) - (- 3 h))$

Factor $- 1$ out of $- (6 f + g) - (- 3 h)$ .

$- (x + y) (x - y) (- (6 f + g - 3 h))$

Remove unnecessary parentheses.

$- (x + y) (x - y) \cdot - 1 (6 f + g - 3 h)$

Combine exponents.

Factor out negative.

$- (((x + y) (x - y)) \cdot - 1 (6 f + g - 3 h))$

Multiply $- 1$ by $- 1$ .

$1 (((x + y) (x - y)) (6 f + g - 3 h))$

Multiply $x + y$ by $1$ .

$(x + y) ((x - y) (6 f + g - 3 h))$

Remove unnecessary parentheses.

$(x + y) (x - y) (6 f + g - 3 h)$

Factor gx^2-3hx^2-6fy^2-gy^2+6fx^2+3hy^2

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