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受欢迎的代数 >

展开 (m-2)(m^2-4)^2(m+2)

解答

展开

(m - 2) (m^{2} - 4)^{2} (m + 2)

解答

m^{6} - 12 m^{4} + 48 m^{2} - 64

求解步骤

(m - 2) (m^{2} - 4)^{2} (m + 2)

= (m^{2} - 4)^{2} (m - 2) (m + 2)

Apply Difference of Two Squares

(m - 2) (m + 2) : m^{2} - 4

= (m^{2} - 4)^{2} (m^{2} - 4)

使用指数法则:

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

(m^{2} - 4)^{2} (m^{2} - 4) = (m^{2} - 4)^{2 + 1}

= (m^{2} - 4)^{2 + 1}

数字相加:

2 + 1 = 3

= (m^{2} - 4)^{3}

使用完全立方公式:

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

(m^{2} - 4)^{3} = (m^{2})^{3} - 3 (m^{2})^{2} \cdot 4 + 3 m^{2} \cdot 4^{2} - 4^{3}

= (m^{2})^{3} - 3 (m^{2})^{2} \cdot 4 + 3 m^{2} \cdot 4^{2} - 4^{3}

化简

(m^{2})^{3} - 3 (m^{2})^{2} \cdot 4 + 3 m^{2} \cdot 4^{2} - 4^{3} : m^{6} - 12 m^{4} + 48 m^{2} - 64

= m^{6} - 12 m^{4} + 48 m^{2} - 64

流行的例子

展开 (3x^2-y^3)^2

e x p an d (3 x^{2} - y^{3})^{2}

化简 (-7+7i)-(3+2i)-(i)

s im pl i f y (- 7 + 7 i) - (3 + 2 i) - (i)

化简 2/(8-sqrt(7))

s im pl i f y \frac{2}{8 - 7}

展开 (2x+3)(2x+5)

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

s im pl i f y \frac{x}{3} + \frac{x}{5}