An engineering model for the structural density ρ \rho\,ρ of a composite material, relative to a depth xxx, is given by the binomial expansion of (3+kx)6(3 + kx)^6(3+kx)6 in ascending powers of xxx. The expansion is written in the form:
ρ=c0+c1x+c2x2+c3x3+…\rho = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + \dotsρ=c0+c1x+c2x2+c3x3+…
where c0,c1,c2, c_0, c_1, c_2,\,c0,c1,c2, and c3 c_3\,c3 are constants.
Find the value of c0c_0c0.
Given that:
Find:
(i) the value of kkk
(ii) the value of c2c_2c2
Practise Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, 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.