展开 (5x-x^3)^2sqrt(8+x^2)

解答

展开

(5 x - x^{3})^{2} 8 + x^{2}

25 x^{2} 8 + x^{2} - 10 x^{4} 8 + x^{2} + x^{6} 8 + x^{2}

求解步骤

(5 x - x^{3})^{2} 8 + x^{2}

展开

(5 x - x^{3})^{2} : 25 x^{2} - 10 x^{4} + x^{6}

= (25 x^{2} - 10 x^{4} + x^{6}) 8 + x^{2}

= 8 + x^{2} (25 x^{2} - 10 x^{4} + x^{6})

使用分配律:

m (a + b + c) = ma + mb + m c

8 + x^{2} (25 x^{2} - 10 x^{4} + x^{6}) = 8 + x^{2} \cdot 25 x^{2} + 8 + x^{2} (- 10 x^{4}) + 8 + x^{2} x^{6}

= 8 + x^{2} \cdot 25 x^{2} + 8 + x^{2} (- 10 x^{4}) + 8 + x^{2} x^{6}

化简

8 + x^{2} \cdot 25 x^{2} + 8 + x^{2} (- 10 x^{4}) + 8 + x^{2} x^{6} : 25 x^{2} 8 + x^{2} - 10 x^{4} 8 + x^{2} + x^{6} 8 + x^{2}

= 25 x^{2} 8 + x^{2} - 10 x^{4} 8 + x^{2} + x^{6} 8 + x^{2}

e x p an d \frac{x ^{2}}{( x + 1 ) ^{3}}

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

e x p an d 6 a^{\frac{7}{4}} \cdot (a^{\frac{7}{4}} + a^{\frac{3}{4}})

e x p an d (3 + 5)^{2}

s im pl i f y (2 x - 5 i)^{2}