khai triển ((5-bx^2)^5)/(10b)

Lời Giải

khai triển

\frac{( 5 - b x ^{2} ) ^{5}}{10 b}

\frac{625}{2 b} - \frac{625 x ^{2}}{2} + 125 b x^{4} - 25 b^{2} x^{6} + \frac{5 b ^{3} x ^{8}}{2} - \frac{b ^{4} x ^{10}}{10}

Các bước giải pháp

\frac{( 5 - b x ^{2} ) ^{5}}{10 b}

(5 - b x^{2})^{5} = 3125 - 3125 b x^{2} + 1250 b^{2} x^{4} - 250 b^{3} x^{6} + 25 b^{4} x^{8} - b^{5} x^{10}

= \frac{3125 - 3125 b x ^{2} + 1250 b ^{2} x ^{4} - 250 b ^{3} x ^{6} + 25 b ^{4} x ^{8} - b ^{5} x ^{10}}{10 b}

Áp dụng quy tắc phân số:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{3125 - 3125 b x ^{2} + 1250 b ^{2} x ^{4} - 250 b ^{3} x ^{6} + 25 b ^{4} x ^{8} - b ^{5} x ^{10}}{10 b} = \frac{3125}{10 b} - \frac{3125 b x ^{2}}{10 b} + \frac{1250 b ^{2} x ^{4}}{10 b} - \frac{250 b ^{3} x ^{6}}{10 b} + \frac{25 b ^{4} x ^{8}}{10 b} - \frac{b ^{5} x ^{10}}{10 b}

= \frac{3125}{10 b} - \frac{3125 b x ^{2}}{10 b} + \frac{1250 b ^{2} x ^{4}}{10 b} - \frac{250 b ^{3} x ^{6}}{10 b} + \frac{25 b ^{4} x ^{8}}{10 b} - \frac{b ^{5} x ^{10}}{10 b}

\frac{3125}{10 b} = \frac{625}{2 b}

\frac{3125 b x ^{2}}{10 b} = \frac{625 x ^{2}}{2}

\frac{1250 b ^{2} x ^{4}}{10 b} = 125 b x^{4}

\frac{250 b ^{3} x ^{6}}{10 b} = 25 b^{2} x^{6}

\frac{25 b ^{4} x ^{8}}{10 b} = \frac{5 b ^{3} x ^{8}}{2}

\frac{b ^{5} x ^{10}}{10 b} = \frac{b ^{4} x ^{10}}{10}

= \frac{625}{2 b} - \frac{625 x ^{2}}{2} + 125 b x^{4} - 25 b^{2} x^{6} + \frac{5 b ^{3} x ^{8}}{2} - \frac{b ^{4} x ^{10}}{10}

e x p an d \frac{9 x ^{2}}{( x ^{3} + 4 ) ^{4}}

e x p an d lo g_{10} (4) x^{2} y

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

s im pl i f y 2 δ (x - 2)

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