A design engineer models the attenuation of a high-frequency signal as it passes through a sequence of 7 capacitive filters. The intensity I I\,I relative to the source is given by I=(1−15x)7\displaystyle I = (1 - \frac{1}{5}x)^7I=(1−51x)7, where x x\,x is a tuning parameter.
Determine the first four terms, in ascending powers of xxx, of the binomial expansion of (1−15x)7\left(1 - \frac{1}{5}x\right)^7(1−51x)7 giving each term in its simplest form.
In a modified circuit, the output signal is scaled such that the final intensity is represented by the expansion of (15x+2)(1−15x)7(15x + 2)\left(1 - \frac{1}{5}x\right)^7(15x+2)(1−51x)7 Find the coefficient of x3 x^3\,x3 in this new expansion, giving your answer as a fraction in simplest form.
Practise Edexcel A Level Maths 4.1 Expanding (1 + x)^n with exam-style questions for A Level Maths. 12 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.