What is expand (1+x/(200pi))(1+x/(20000pi)) ?

The solution to expand (1+x/(200pi))(1+x/(20000pi)) is (x^2)/(4000000pi^2)+(101x)/(20000pi)+1

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expand (1+x/(200pi))(1+x/(20000pi))

expand

(1 + \frac{x}{200 π}) (1 + \frac{x}{20000 π})

\frac{x ^{2}}{4000000 π ^{2}} + \frac{101 x}{20000 π} + 1

Solution steps

(1 + \frac{x}{200 π}) (1 + \frac{x}{20000 π})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = \frac{x}{200 π}, c = 1, d = \frac{x}{20000 π}

= 1 \cdot 1 + 1 \cdot \frac{x}{20000 π} + \frac{x}{200 π} \cdot 1 + \frac{x}{200 π} \cdot \frac{x}{20000 π}

= 1 \cdot 1 + 1 \cdot \frac{x}{20000 π} + 1 \cdot \frac{x}{200 π} + \frac{x}{200 π} \cdot \frac{x}{20000 π}

Simplify

1 \cdot 1 + 1 \cdot \frac{x}{20000 π} + 1 \cdot \frac{x}{200 π} + \frac{x}{200 π} \cdot \frac{x}{20000 π} : \frac{x ^{2}}{4000000 π ^{2}} + \frac{101 x}{20000 π} + 1

= \frac{x ^{2}}{4000000 π ^{2}} + \frac{101 x}{20000 π} + 1

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What is expand (1+x/(200pi))(1+x/(20000pi)) ?
The solution to expand (1+x/(200pi))(1+x/(20000pi)) is (x^2)/(4000000pi^2)+(101x)/(20000pi)+1