What is expand (x/(10)(100-5y))*y ?

The solution to expand (x/(10)(100-5y))*y is -(xy^2)/2+10xy

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expand (x/(10)(100-5y))*y

expand

(\frac{x}{10} (100 - 5 y)) \cdot y

- \frac{x y ^{2}}{2} + 10 x y

Solution steps

(\frac{x}{10} (100 - 5 y)) y

Remove parentheses:

(a) = a

= \frac{x}{10} (100 - 5 y) y

Multiply fractions:

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

= \frac{x ( 100 - 5 y ) y}{10}

Factor

100 - 5 y : 5 (20 - y)

= \frac{x \cdot 5 ( 20 - y ) y}{10}

Cancel the common factor:

5

= \frac{x y ( - y + 20 )}{2}

Expand

x y (- y + 20) : - x y^{2} + 20 x y

= \frac{- x y ^{2} + 20 x y}{2}

Apply the fraction rule:

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

\frac{- x y ^{2} + 20 x y}{2} = - \frac{x y ^{2}}{2} + \frac{20 x y}{2}

= - \frac{x y ^{2}}{2} + \frac{20 x y}{2}

Divide the numbers:

\frac{20}{2} = 10

= - \frac{x y ^{2}}{2} + 10 x y

\frac{x + 4}{( x + 1 ) ^{2}}

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

(x - \frac{π}{2}) tan (x)

x y^{4} d x + (y^{2} + 2) e^{- 3 x} d y

What is expand (x/(10)(100-5y))*y ?
The solution to expand (x/(10)(100-5y))*y is -(xy^2)/2+10xy