展开 (sqrt(3)x-1)^3

解答

展开

(3 x - 1)^{3}

33 x^{3} - 9 x^{2} + 33 x - 1

求解步骤

(3 x - 1)^{3}

使用完全立方公式:

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

(3 x - 1)^{3} = (3 x)^{3} - 3 (3 x)^{2} \cdot 1 + 33 x \cdot 1^{2} - 1^{3}

= (3 x)^{3} - 3 (3 x)^{2} \cdot 1 + 33 x \cdot 1^{2} - 1^{3}

化简

(3 x)^{3} - 3 (3 x)^{2} \cdot 1 + 33 x \cdot 1^{2} - 1^{3} : 33 x^{3} - 9 x^{2} + 33 x - 1

= 33 x^{3} - 9 x^{2} + 33 x - 1

e x p an d \frac{16 x ^{2} + 40}{( x ^{2} + 0.8 x + 4 ) ( x ^{2} + 1 ) ( x ^{2} + 4 )}

e x p an d (x 32 + y 3)^{3}

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