What is expand (x^2+5x+6)(1/2 sin(2x)) ?

The solution to expand (x^2+5x+6)(1/2 sin(2x)) is (sin(2x)x^2+5sin(2x)x)/2+3sin(2x)

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expand (x^2+5x+6)(1/2 sin(2x))

expand

(x^{2} + 5 x + 6) (\frac{1}{2} sin (2 x))

\frac{sin ( 2 x ) x ^{2} + 5 sin ( 2 x ) x}{2} + 3 sin (2 x)

Solution steps

(x^{2} + 5 x + 6) (\frac{1}{2} sin (2 x))

= (\frac{1}{2} sin (2 x)) (x^{2} + 5 x + 6)

Apply the distributive law:

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

(\frac{1}{2} sin (2 x)) (x^{2} + 5 x + 6) = \frac{1}{2} sin (2 x) x^{2} + \frac{1}{2} sin (2 x) \cdot 5 x + \frac{1}{2} sin (2 x) \cdot 6

= \frac{1}{2} sin (2 x) x^{2} + \frac{1}{2} sin (2 x) \cdot 5 x + \frac{1}{2} sin (2 x) \cdot 6

Simplify

\frac{1}{2} sin (2 x) x^{2} + \frac{1}{2} sin (2 x) \cdot 5 x + \frac{1}{2} sin (2 x) \cdot 6 : \frac{sin ( 2 x ) x ^{2} + 5 sin ( 2 x ) x}{2} + 3 sin (2 x)

= \frac{sin ( 2 x ) x ^{2} + 5 sin ( 2 x ) x}{2} + 3 sin (2 x)

\frac{\partial}{\partial x} ((z) (4 x yz - e^{z}))

\frac{4 s}{( s - 1 ) ( s + 1 ) ^{2}}

\frac{7 + 2 s + 6 e ^{- 4 s}}{( s + 2 ) ( s + 6 )}

(x + \frac{1}{6}) (x - \frac{1}{3})

\frac{e ^{x} x - 2 e ^{x}}{( x - 1 ) ^{2}}

What is expand (x^2+5x+6)(1/2 sin(2x)) ?
The solution to expand (x^2+5x+6)(1/2 sin(2x)) is (sin(2x)x^2+5sin(2x)x)/2+3sin(2x)