zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

因式分解 gx^2-3hx^2-6fy^2-gy^2+6fx^2+3hy^2

解答

因式分解

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

解答

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

求解步骤

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

因式分解出通项

g

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

分解

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}

因式分解出通项

3 h

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

分解

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)

改写为

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

因式分解出通项

(x - y) (x + y)

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

因式分解出通项

6 f

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

分解

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

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

改写为

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

因式分解出通项

(x - y) (x + y)

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

流行的例子

(x-3)(x+4)=(x+2)^2-1

(x - 3) (x + 4) = (x + 2)^{2} - 1

8 n < - 88

x + 4 > - 15

化简 100000^{1/5}

s im pl i f y 10000 0^{\frac{1}{5}}

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