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受欢迎的代数 >

因式分解 16x^4-y^4

解答

因式分解

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

解答

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

求解步骤

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

16 x^{4} = (4 x^{2})^{2}

y^{4} = (y^{2})^{2}

= (4 x^{2})^{2} - (y^{2})^{2}

使用平方差公式:

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

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

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

因式分解

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

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

流行的例子

4/5 x+6/5 =-2/5

\frac{4}{5} x + \frac{6}{5} = - \frac{2}{5}

\frac{- 4}{3} = \frac{x}{6}

s - (- 3) = - 11

x - 4 < 7

(x - 1) (x - 7) = 0