Asoap bubble had rainbow-colors and broke after forming a colorless part. what is the name of “colorless part”? calculate its thickness as “a water film (n = 1.333) in air (n = 1)”. [*visible range is 400 – 800 nm.]

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The best way to learn this is to multiply out the terms of (d – 4b)^3. First do (d – 4b)^2, then multiply that by (d – 4b). Collect all the terms that have the same powers of d and b. Then arrange them by decreasing powers of d. 
First 2 terms are d^3 and - 3d^2(4b) 
 (d - 4b)³ = (3C0)*(-4b)³ + (3C1)*(d)*(-4b)² + (3C2)*(d²)*(-4b) + (3C3)*(d³) 

= -64b³ + 48*d*(b²) - 12*(d²)*b + d³

Ibelieve the answer is b. dugout