Additional Mathematics 0606: BINOMIAL THEOREM Topical Past Paper Questions

(a) Expand $ (1+2x)(1-2x) $. [1] (b) Hence find the coefficient of $ x^{5} $ in the expansion of $ (1+2x)^{10}(1-2x)^{12} $. [4]

Find the exact value of the term independent of x in the expansion of $$ \left(2+\frac{3}{x^{2}}\right)^{10}\left(1-4x^{2}\right)^{2}.\quad[6] $$

The expansion of $ \left(a+\frac{x}{a}\right)^n $ in ascending powers of x begins $ b^4+48b^3x $, where n, a and b are positive integers. (a) Show that $ a^{\frac{n}{2}-4}=\left(\frac{48}{n}\right)^2 $. [4] (b) Given also that the third term is $ 1056b^{2}x^{2} $, find the values…