4.2 Expanding (a + bx)^n

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The population $P (t)$ , in thousands, of a species in a controlled environment is estimated using the model $P(t)=15(25+At)−12\displaystyle P(t) = 15(25 + At)^{-\frac{1}{2}}$ , where $t\,$ is the time in years since the study began ( $\ge 0$ ). The binomial expansion of $P (t)$ in ascending powers of $t\,$ is given as $B−625t+Ct2+…\displaystyle B - \frac{6}{25}t + Ct^2 + \dots$

Determine the exact values of the constants $A$ , $B$ , and $C$ .

[5]

State the range of values of $t\,$ for which this expansion is valid.

[1]

For the expansion, find the coefficient of the term in $t^3$ .

[2]

4.2 Expanding (a + bx)^n Questions

Practise Edexcel A Level Maths 4.2 Expanding (a + bx)^n with exam-style questions for A Level Maths. 99 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.