SingaporeAdditional MathematicsQuick questions

Binomial Theorem and Partial Fractions

Quick questions on Finding a particular term in a binomial expansion explained: O-Level A-Maths

8short 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?

Show answer

The term in

(a + b)^n

that contains

b^r

is:

What is finding the coefficient of a given power?

Show answer

To find the coefficient of

x^k

, work out which power of

x

the general term produces, set that equal to

k

, and solve for

r

. Then substitute

r

back to evaluate the coefficient. The power of

x

comes from both

a^{n-r}

and

b^r

if either contains

x

What is combining powers of x?

Show answer

When both parts of the bracket contain

x

(for example

x

and

\dfrac{2}{x}

), use the index laws to combine them into a single power of

x

What is the term independent of x?

Show answer

The term independent of

x

is the constant term, where the power of

x

is zero. Set the combined exponent equal to

0

, solve for

r

, and evaluate that term.

What is sign of a negative term?

Show answer

With

b = -\dfrac{1}{x}

, the factor

(-1)^r

alternates the sign; include it.

What is q1?

Show answer

Write the general term of

(1 + x)^8

. [1 mark]

What is q2?

Show answer

Find the coefficient of

x^2

(1 + 3x)^5

. [3 marks]

What is q3?

Show answer

Find the term independent of

x

\left(x - \dfrac{1}{x}\right)^4

. [3 marks]

All Additional MathematicsQ&A pages