What is expand-((w)(L+x)^2)/2+(2Lwx) ?

The solution to expand-((w)(L+x)^2)/2+(2Lwx) is -(wL^2)/2-(wx^2)/2+wLx

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expand-((w)(L+x)^2)/2+(2Lwx)

expand

- \frac{( w ) ( L + x ) ^{2}}{2} + (2 L w x)

- \frac{w L ^{2}}{2} - \frac{w x ^{2}}{2} + w Lx

Solution steps

- \frac{( w ) ( L + x ) ^{2}}{2} + (2 L w x)

Remove parentheses:

(a) = a

= - \frac{w ( L + x ) ^{2}}{2} + 2 L w x

\frac{w ( L + x ) ^{2}}{2} = \frac{w L ^{2} + 2 w Lx + w x ^{2}}{2}

= - \frac{w L ^{2} + 2 w Lx + w x ^{2}}{2} + 2 w Lx

Convert element to fraction:

2 w Lx = \frac{2 L w x 2}{2}

= - \frac{w L ^{2} + 2 w Lx + w x ^{2}}{2} + \frac{2 L w x \cdot 2}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{- ( w L ^{2} + 2 w Lx + w x ^{2} ) + 2 L w x \cdot 2}{2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{- ( w L ^{2} + 2 w Lx + w x ^{2} ) + 4 w Lx}{2}

Expand

- (w L^{2} + 2 w Lx + w x^{2}) + 4 L w x : - w L^{2} - w x^{2} + 2 w Lx

= \frac{- w L ^{2} - w x ^{2} + 2 w Lx}{2}

Apply the fraction rule:

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

\frac{- w L ^{2} - w x ^{2} + 2 w Lx}{2} = - \frac{w L ^{2}}{2} - \frac{w x ^{2}}{2} + \frac{2 w Lx}{2}

= - \frac{w L ^{2}}{2} - \frac{w x ^{2}}{2} + \frac{2 w Lx}{2}

Divide the numbers:

\frac{2}{2} = 1

= - \frac{w L ^{2}}{2} - \frac{w x ^{2}}{2} + w Lx

\frac{d}{d x} ((t) (x^{2} + y^{2} - z (t)^{2}))

(2 (y \cdot v)) (d y \cdot v + y \cdot d v)

\frac{arccosh ( e ^{- x} )}{e ^{- x}}

\frac{1}{( s + 9 ) ( s ^{2} + k ^{2} )}

What is expand-((w)(L+x)^2)/2+(2Lwx) ?
The solution to expand-((w)(L+x)^2)/2+(2Lwx) is -(wL^2)/2-(wx^2)/2+wLx