因式分解 27a^3-27a^2+9a-1

解答

因式分解

27 a^{3} - 27 a^{2} + 9 a - 1

(3 a - 1)^{3}

求解步骤

27 a^{3} - 27 a^{2} + 9 a - 1

使用有理根定理

= (3 a - 1) \frac{27 a ^{3} - 27 a ^{2} + 9 a - 1}{3 a - 1}

\frac{27 a ^{3} - 27 a ^{2} + 9 a - 1}{3 a - 1} = 9 a^{2} - 6 a + 1

= (3 a - 1) (9 a^{2} - 6 a + 1)

因式分解

9 a^{2} - 6 a + 1 : (3 a - 1) (3 a - 1)

= (3 a - 1) (3 a - 1) (3 a - 1)

使用指数法则:

aaa = a^{3}

(3 a - 1) (3 a - 1) (3 a - 1) = (3 a - 1)^{3}

= (3 a - 1)^{3}

s im pl i f y (\frac{- ( x ^{2} \cdot y ^{4} )}{( x \cdot y ^{- 2} )})^{3}

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

s im pl i f y \frac{1}{16} \cdot x^{2} \cdot y^{6} + \frac{1}{6} \cdot x \cdot y^{3} + \frac{1}{9}

f a c t or 8 a^{3} + y^{3}

s im pl i f y 34568 \frac{( sec ( a ) )}{( tan ( a ) + cot ( a ) )}