展开 (sqrt(x)+\sqrt[3]{x})(x-1)^3

解答

展开

(x + 3 x) (x - 1)^{3}

x^{3} x + x^{3} 3 x - 3 x^{2} x - 3 x^{2} 3 x + 3 x x + 3 x 3 x - x - 3 x

求解步骤

(x + 3 x) (x - 1)^{3}

= (x - 1)^{3} (x + 3 x)

展开

(x - 1)^{3} : x^{3} - 3 x^{2} + 3 x - 1

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

打开括号

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

化简

x^{3} x + x^{3} 3 x - 3 x^{2} x - 3 x^{2} 3 x + 3 x x + 3 x 3 x - 1 \cdot x - 1 \cdot 3 x : x^{3} x + x^{3} 3 x - 3 x^{2} x - 3 x^{2} 3 x + 3 x x + 3 x 3 x - x - 3 x

= x^{3} x + x^{3} 3 x - 3 x^{2} x - 3 x^{2} 3 x + 3 x x + 3 x 3 x - x - 3 x

e x p an d π \cdot (- 14 \cdot r + 64) \cdot r^{2}

s im pl i f y (x - 1 + 3) (x + 1 + 3)

e x p an d \frac{( ( n + 1 ) ^{2} \cdot ( n + 2 ) ^{2} )}{4}

e x p an d δ (n) \cdot x (n - 1)

e x p an d 7 l e f (t, a) t (a + 5) - 3 0^{^{'}}