SingaporeAdditional MathematicsQuick questions

Binomial Theorem and Partial Fractions

Quick questions on Finding a particular term in a binomial expansion: N(A)-Level Additional Mathematics

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is the general term?

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In the expansion of

(a + b)^n

, the term containing

b^r

is:

What is finding a constant (term independent of x)?

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A constant term is the term in

x^0

. Combine the powers of

x

as before, set the total power to zero, solve for

r

, and evaluate. This is common when the bracket contains both

x

and

\dfrac{1}{x}

, because the powers can cancel.

What is not combining the powers of x first?

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When the bracket has both

x

and

\tfrac{1}{x}

, simplify to a single power

x^{n - 2r}

(or similar) before setting it equal to the target.

What is sign slips with a negative term?

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b

is negative, the sign of

b^r

alternates with

r

; track it.

What is q1?

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Write down the general term of

(1 + x)^n

. [1 mark]

What is q2?

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Find the coefficient of

x^2

(1 + x)^5

. [2 marks]

What is q3?

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Find the coefficient of

x^3

(1 + 2x)^4

. [3 marks]

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