因式分解 343v^3+27w^6

解答

因式分解

343 v^{3} + 27 w^{6}

(7 v + 3 w^{2}) (49 v^{2} - 21 v w^{2} + 9 w^{4})

求解步骤

343 v^{3} + 27 w^{6}

使用指数运算法则

= (7 v)^{3} + (3 w^{2})^{3}

使用立方和公式:

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

(7 v)^{3} + (3 w^{2})^{3} = (7 v + 3 w^{2}) ((7 v)^{2} - 7 v \cdot 3 w^{2} + (3 w^{2})^{2})

= (7 v + 3 w^{2}) ((7 v)^{2} - 7 v \cdot 3 w^{2} + (3 w^{2})^{2})

化简

(7 v)^{2} - 7 v \cdot 3 w^{2} + (3 w^{2})^{2} : 49 v^{2} - 21 v w^{2} + 9 w^{4}

= (7 v + 3 w^{2}) (49 v^{2} - 21 v w^{2} + 9 w^{4})

s im pl i f y (- 2)^{2} + (3)^{2}

f a c t or 5 x^{3} - 15 x^{2} y

f a c t or 3 x^{3} - 9 x^{2}

e x p an d (2 x + 4) (3 x - 5)

f a c t or ab - a^{3} b^{3}