因式分解 1/16 x^4-y^4

解答

因式分解

\frac{1}{16} x^{4} - y^{4}

(\frac{x}{2} + y) (\frac{x}{2} - y) (\frac{x ^{2}}{4} + y^{2})

求解步骤

\frac{1}{16} x^{4} - y^{4}

将

\frac{x ^{4}}{16} - y^{4}

改写为

(\frac{1}{16} x^{2})^{2} - (y^{2})^{2}

= (\frac{1}{16} x^{2})^{2} - (y^{2})^{2}

使用平方差公式:

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

(\frac{1}{16} x^{2})^{2} - (y^{2})^{2} = (\frac{1}{16} x^{2} + y^{2}) (\frac{1}{16} x^{2} - y^{2})

= (\frac{1}{16} x^{2} + y^{2}) (\frac{1}{16} x^{2} - y^{2})

分解

\frac{1}{16} x^{2} - y^{2} : \frac{1}{16} x + y \frac{1}{16} x - y

= (\frac{1}{16} x^{2} + y^{2}) \frac{1}{16} x + y \frac{1}{16} x - y

整理后得

= (\frac{x}{2} + y) (\frac{x}{2} - y) (\frac{x ^{2}}{4} + y^{2})

f (h) = 4 h^{(3)} + 10 h^{(2)} - 8 h + 17

f a c t or x (\frac{1}{2} x^{2} - 1)

f a c t or 6 p m + 4 p n - 3 m q - 2 n q

f a c t or x^{'} 2 - 36

f a c t or [R u N_{(5)} (H_{(2)} O)] C l_{(2)}