展开 (ax^2+bx)(dcos(x)+esin(x))

解答

展开

(a x^{2} + b x) (d cos (x) + e sin (x))

a d x^{2} cos (x) + e a x^{2} sin (x) + b d x cos (x) + e b x sin (x)

求解步骤

(a x^{2} + b x) (d cos (x) + e sin (x))

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = a x^{2}, b = b x, c = d cos (x), d = e sin (x)

= a x^{2} d cos (x) + a x^{2} e sin (x) + b x d cos (x) + b x e sin (x)

= a d x^{2} cos (x) + e a x^{2} sin (x) + b d x cos (x) + e b x sin (x)

e x p an d \frac{x ^{2} + 20 x + 1}{( x + 1 ) ^{2}}

e x p an d 4 e^{x} (e^{2 x} - e^{x})

e x p an d l im x \Rightarrow 2 (3 x^{2} - 5 x + 2)

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

e x p an d \frac{( r x H - x q y ) H}{G}