The first three terms, in ascending powers of xxx, of the binomial expansion of (16+5x)12(16 + 5x)^{\frac{1}{2}}(16+5x)21 are given by (16+5x)12≈a+58x−25512x2(16 + 5x)^{\frac{1}{2}} \approx a + \frac{5}{8}x - \frac{25}{512}x^2(16+5x)21≈a+85x−51225x2 where aaa is a constant.
State the range of values of xxx for which this expansion is valid.
Choose from the options below: ∣x∣<516∣x∣<165∣x∣<4∣x∣<1|x| < \frac{5}{16} \quad |x| < \frac{16}{5} \quad |x| < 4 \quad |x| < 1∣x∣<165∣x∣<516∣x∣<4∣x∣<1
Find the value of aaa.
Choose from the options below: 148161 \quad 4 \quad 8 \quad 1614816
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.