What is (x/2+3y)(x/4+2y) ?

The solution to (x/2+3y)(x/4+2y) is ((6y+x)(8y+x))/8

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simplify (x/2+3y)(x/4+2y)

simplify

(\frac{x}{2} + 3 y) (\frac{x}{4} + 2 y)

\frac{( 6 y + x ) ( 8 y + x )}{8}

Solution steps

(\frac{x}{2} + 3 y) (\frac{x}{4} + 2 y)

Join

\frac{x}{2} + 3 y : \frac{6 y + x}{2}

= \frac{6 y + x}{2} (\frac{x}{4} + 2 y)

Join

\frac{x}{4} + 2 y : \frac{8 y + x}{4}

= \frac{6 y + x}{2} \cdot \frac{8 y + x}{4}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( 6 y + x ) ( 8 y + x )}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{( 6 y + x ) ( 8 y + x )}{8}

ln (5) \cdot 5 (6 x^{2} - x + 2) \cdot (12 x - 1)

7 (π - 5)

\frac{5 ( 19 - 1 )}{9}

5 (\frac{x ^{2}}{3} + 2 x + 4)

- (2 x + 1) sin (x^{2} + x)