展开 6x^5(2x^2+9x-6)^2

解答

展开

6 x^{5} (2 x^{2} + 9 x - 6)^{2}

24 x^{9} + 216 x^{8} + 342 x^{7} - 648 x^{6} + 216 x^{5}

求解步骤

6 x^{5} (2 x^{2} + 9 x - 6)^{2}

(2 x^{2} + 9 x - 6)^{2} = 4 x^{4} + 36 x^{3} + 57 x^{2} - 108 x + 36

= 6 x^{5} (4 x^{4} + 36 x^{3} + 57 x^{2} - 108 x + 36)

打开括号

= 6 x^{5} \cdot 4 x^{4} + 6 x^{5} \cdot 36 x^{3} + 6 x^{5} \cdot 57 x^{2} + 6 x^{5} (- 108 x) + 6 x^{5} \cdot 36

使用加减运算法则

+ (- a) = - a

= 6 \cdot 4 x^{5} x^{4} + 6 \cdot 36 x^{5} x^{3} + 6 \cdot 57 x^{5} x^{2} - 6 \cdot 108 x^{5} x + 6 \cdot 36 x^{5}

化简

6 \cdot 4 x^{5} x^{4} + 6 \cdot 36 x^{5} x^{3} + 6 \cdot 57 x^{5} x^{2} - 6 \cdot 108 x^{5} x + 6 \cdot 36 x^{5} : 24 x^{9} + 216 x^{8} + 342 x^{7} - 648 x^{6} + 216 x^{5}

= 24 x^{9} + 216 x^{8} + 342 x^{7} - 648 x^{6} + 216 x^{5}

e x p an d 5 (e^{\frac{x}{10}} + e^{- \frac{x}{10}})

e x p an d (e^{x} + e^{-} x)^{4}

e x p an d \frac{1}{( 1 + x ) ( 1 - x )}

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

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