What is expand ((100x+1)(25x+1))/(2500) ?

The solution to expand ((100x+1)(25x+1))/(2500) is x^2+x/(20)+1/2500

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expand ((100x+1)(25x+1))/(2500)

expand

\frac{( 100 x + 1 ) ( 25 x + 1 )}{2500}

x^{2} + \frac{x}{20} + \frac{1}{2500}

Solution steps

\frac{( 100 x + 1 ) ( 25 x + 1 )}{2500}

Expand

(100 x + 1) (25 x + 1) : 2500 x^{2} + 125 x + 1

= \frac{2500 x ^{2} + 125 x + 1}{2500}

Apply the fraction rule:

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

\frac{2500 x ^{2} + 125 x + 1}{2500} = \frac{2500 x ^{2}}{2500} + \frac{125 x}{2500} + \frac{1}{2500}

= \frac{2500 x ^{2}}{2500} + \frac{125 x}{2500} + \frac{1}{2500}

Divide the numbers:

\frac{2500}{2500} = 1

= x^{2} + \frac{125 x}{2500} + \frac{1}{2500}

Cancel

\frac{125 x}{2500} : \frac{x}{20}

= x^{2} + \frac{x}{20} + \frac{1}{2500}

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What is expand ((100x+1)(25x+1))/(2500) ?
The solution to expand ((100x+1)(25x+1))/(2500) is x^2+x/(20)+1/2500