化简 3(x-2)(4-3x)^2(25-x^2)^2

解答

化简

3 (x - 2) (4 - 3 x)^{2} (25 - x^{2})^{2}

3 (x - 2) (- 3 x + 4)^{2} (- x^{2} + 25)^{2}

求解步骤

3 (x - 2) (4 - 3 x)^{2} (25 - x^{2})^{2}

使用指数法则:

a^{m} b^{m} = (ab)^{m},

假定

a \geq 0, b \geq 0

(- 3 x + 4)^{2} (- x^{2} + 25)^{2} = ((- 3 x + 4) (- x^{2} + 25))^{2}

= 3 (x - 2) ((- 3 x + 4) (- x^{2} + 25))^{2}

((4 - 3 x) (25 - x^{2}))^{2} = (4 - 3 x)^{2} (25 - x^{2})^{2}

= 3 (x - 2) (- 3 x + 4)^{2} (- x^{2} + 25)^{2}

s im pl i f y 2 t (2 t^{2})

s im pl i f y 6200 (1.041)^{- 6}

s im pl i f y e^{- x} (e^{3 x} + 6)

s im pl i f y 3 e (e^{- x})

s im pl i f y (854050) (2.5 \cdot 1 0^{- 6})