因式分解 y^6+27x^3

解答

因式分解

y^{6} + 27 x^{3}

(y^{2} + 3 x) (y^{4} - 3 y^{2} x + 9 x^{2})

求解步骤

y^{6} + 27 x^{3}

使用指数运算法则

= (y^{2})^{3} + (3 x)^{3}

使用立方和公式:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

(y^{2})^{3} + (3 x)^{3} = (y^{2} + 3 x) ((y^{2})^{2} - y^{2} \cdot 3 x + (3 x)^{2})

= (y^{2} + 3 x) ((y^{2})^{2} - y^{2} \cdot 3 x + (3 x)^{2})

化简

(y^{2})^{2} - y^{2} \cdot 3 x + (3 x)^{2} : y^{4} - 3 y^{2} x + 9 x^{2}

= (y^{2} + 3 x) (y^{4} - 3 y^{2} x + 9 x^{2})

e x p an d (x^{2} + 1) \cdot sin (x)

s im pl i f y \frac{e ^{t} an x - e ^{s} in x}{( tan ^{2} ( x ) ) ^{3}}

s im pl i f y 3 x + 8 x^{5} - x + 9 x^{2} - 6 x^{2}

s im pl i f y 4 (m^{- 1} n)

f a c t or x^{2} + 13 x y - 30 y^{2}