What is expand ((a+b)(c+2d+3))/4 ?

The solution to expand ((a+b)(c+2d+3))/4 is (ac)/4+(ad)/2+(3a)/4+(bc)/4+(bd)/2+(3b)/4

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expand ((a+b)(c+2d+3))/4

expand

\frac{( a + b ) ( c + 2 d + 3 )}{4}

\frac{a c}{4} + \frac{a d}{2} + \frac{3 a}{4} + \frac{b c}{4} + \frac{b d}{2} + \frac{3 b}{4}

Solution steps

\frac{( a + b ) ( c + 2 d + 3 )}{4}

Expand

(a + b) (c + 2 d + 3) : a c + 2 a d + 3 a + b c + 2 b d + 3 b

= \frac{a c + 2 a d + 3 a + b c + 2 b d + 3 b}{4}

Apply the fraction rule:

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

\frac{a c + 2 a d + 3 a + b c + 2 b d + 3 b}{4} = \frac{a c}{4} + \frac{2 a d}{4} + \frac{3 a}{4} + \frac{b c}{4} + \frac{2 b d}{4} + \frac{3 b}{4}

= \frac{a c}{4} + \frac{2 a d}{4} + \frac{3 a}{4} + \frac{b c}{4} + \frac{2 b d}{4} + \frac{3 b}{4}

Cancel

\frac{2 a d}{4} : \frac{a d}{2}

= \frac{a c}{4} + \frac{a d}{2} + \frac{3 a}{4} + \frac{b c}{4} + \frac{2 b d}{4} + \frac{3 b}{4}

Cancel

\frac{2 b d}{4} : \frac{b d}{2}

= \frac{a c}{4} + \frac{a d}{2} + \frac{3 a}{4} + \frac{b c}{4} + \frac{b d}{2} + \frac{3 b}{4}

e^{x^{3} - 3 x} (3 x^{2} - 3)

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

D x [(x - 1) (4 - 2 x)]

(x + 1) \cdot e^{x}

\frac{5 ( q ^{6} - 3 q ^{4} + 3 q ^{2} )}{3}

What is expand ((a+b)(c+2d+3))/4 ?
The solution to expand ((a+b)(c+2d+3))/4 is (ac)/4+(ad)/2+(3a)/4+(bc)/4+(bd)/2+(3b)/4