2.2: Binomial expansion applied to an exponential equation

0606/21/M/J/20 — Question 8 · 7 marks · Binomial, Exponentials, Equations

(a)
Expand (2x)5(2 - x)^{5}, simplifying each coefficient.
[3]
(b)
Hence solve e(2x)5×e80xe10x4+32=ex5\dfrac{e^{(2-x)^{5}} \times e^{80x}}{e^{10x^{4}} + 32} = e^{-x^{5}}.
[4]