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Popular Algebra >

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

Solution

factor

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

Solution

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

Solution steps

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

Factor out common term

g

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

Factor

x^{2} - y^{2} : (x + y) (x - y)

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

Factor out common term

3 h

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

Factor

y^{2} - x^{2} : (y + x) (y - x)

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

Rewrite as

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

Factor out common term

(x - y) (x + y)

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

Factor out common term

6 f

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

Factor

x^{2} - y^{2} : (x + y) (x - y)

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

Rewrite as

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

Factor out common term

(x - y) (x + y)

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

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5 x^{2} + 5 x - 30 = 0

Frequently Asked Questions (FAQ)

What is factor gx^2-3hx^2-6fy^2-gy^2+6fx^2+3hy^2 ?
The solution to factor gx^2-3hx^2-6fy^2-gy^2+6fx^2+3hy^2 is (x-y)(x+y)(g-3h+6f)

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