CAIE A-Level Mathematics 1.6.1 Binomial expansion

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise expanding (a + b)^n, selecting powers of x, and using binomial coefficients to find constants, coefficients or parameters.

How this is tested

choose the binomial term that gives the required power before forming its coefficient
combine expansion terms with another factor before equating coefficients for constants

(a)

Expand $\left(2-\frac{1}{2} x\right)^{6}$ in ascending powers of x up to and including the term in $x^{3}$ .

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(b)

Hence find the coefficient of $x^{3}$ in the expansion of $\left(3-x+2 x^{3}\right)\left(2-\frac{1}{2} x\right)^{6}$ .

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