CAIE A-Level Mathematics AS 1.6.1 Binomial Expansion Questions

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

Exam points

Expand a binomial (a + b)^n for a positive integer n using binomial coefficients, in ascending or descending powers and to a stated term or to completion.
Select the term with a specified power, including the constant term, in binomial expansions containing powers of x or 1/x.
Use specified coefficients or relationships between expansions to determine unknown constants and coefficients, including products or sums of expansions.

[Maximum number: 4]

Find the coefficient of $x^{2}$ in the expansion of

(2-5 x)(1+3 x)^{10}

Correct second term 30 x in expansion of $(1+3 x)^{10}$
WWW, may be implied later.

Correct third term $+405 x^{2}$
Marking guidance:

Ignore subsequent terms, may be implied later.

Multiply (2-5x) by their $30 x+405 x^{2}$ to obtain two $x^{2}$ terms only
Expect $-150 x^{2}, 810 x^{2}$ .

Coefficient is 660
Must be clearly identified.
Allow final answer $660 x^{2}$ .

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CAIE A-Level Mathematics AS 1.6.1 Binomial Expansion Questions question 1