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受欢迎的代数 >

化简 ((4a^4-8a^2b^2+4b^4))/((a^2b-b^3))

解答

化简

\frac{( 4 a ^{4} - 8 a ^{2} \cdot b ^{2} + 4 b ^{4} )}{( a ^{2} \cdot b - b ^{3} )}

解答

\frac{4 ( a + b ) ( a - b )}{b}

求解步骤

\frac{4 a ^{4} - 8 a ^{2} b ^{2} + 4 b ^{4}}{a ^{2} b - b ^{3}}

因式分解

4 a^{4} - 8 a^{2} b^{2} + 4 b^{4} : 4 (a + b)^{2} (a - b)^{2}

= \frac{4 ( a + b ) ^{2} ( a - b ) ^{2}}{a ^{2} b - b ^{3}}

因式分解

a^{2} b - b^{3} : b (a + b) (a - b)

= \frac{4 ( a + b ) ^{2} ( a - b ) ^{2}}{b ( a + b ) ( a - b )}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(a + b)^{2} = (a + b) (a + b)

= \frac{4 ( a + b ) ( a + b ) ( a - b ) ^{2}}{b ( a + b ) ( a - b )}

约分:

a + b

= \frac{4 ( a + b ) ( a - b ) ^{2}}{b ( a - b )}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(a - b)^{2} = (a - b) (a - b)

= \frac{4 ( a + b ) ( a - b ) ( a - b )}{b ( a - b )}

约分:

a - b

= \frac{4 ( a + b ) ( a - b )}{b}

流行的例子

化简 (3+8)*x^6-42-7

s im pl i f y (3 + 8) \cdot x^{6} - 42 - 7

因式分解 x^7y^7-xy

f a c t or x^{7} y^{7} - x y

因式分解 2x^2-3xy-2y^2

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

展开 (x-y)^{10}

e x p an d (x - y)^{10}

因式分解 p^2-q^2-p-q

f a c t or p^{2} - q^{2} - p - q