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Binomial Theorem · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SBinomial expansion and coefficients6 marksPaper 2~9 min

A triangular pattern of numbers is shown below, where each row corresponds to the coefficients of

(a+b)^n

\begin{array}{c} \text{Row 0: } 1 \\ \text{Row 1: } 1 \quad 1 \\ \text{Row 2: } 1 \quad 2 \quad 1 \\ \text{Row 3: } 1 \quad 3 \quad 1 \\ \text{Row 4: } 1 \quad 4 \quad 6 \quad 4 \quad 1 \end{array}

(a)

State the numbers in Row 5 of Pascal's triangle. [1 mark]

(b)

Hence, expand

(2x - 3y)^5

in descending powers of

x

. Give all coefficients in simplified form. [3 marks]

(c)

Using your expansion from part (b), find the value of

k

such that the coefficient of

x^3 y^2

in the expansion of

(1 + k)(2x - 3y)^5

is equal to

2880

. [2 marks]

Solutions

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