CAIE IGCSE Additional Math 12.1 binomial theorem

Use this binomial-theorem page to expand expressions, simplify coefficients and keep terms in the requested powers of x.

Exam points

Find first non-zero terms in a binomial expansion in ascending powers.
Simplify each coefficient as an integer, rational number or exact expression.
Handle inner powers such as x² or e^(2x) while forming each binomial term.

[Maximum number: 4]

(a)

Find the first three terms in the expansion of $\left(1+\frac{x}{7}\right)^5$ , in ascending powers of x. Simplify the coefficient of each term.

[ 2 ]

$1+\frac57x+\frac{10}{49}x^2$
B2
B1 for any two correct terms or for the three terms listed but not summed

(b)

The expansion of $7(1+x)^n\left(1+\frac{x}{7}\right)^5$ , where n is a positive integer, is written in ascending powers of x. The first two terms in the expansion are 7+89x. Find the value of n.

[ 2 ]

12
B2
B1 for 7n+5=89 or $7(n+\frac57)=89$ oe or ${}^nC_1=12$

All question bank results loaded

12.1. Use the binomial theorem question 1

Question (a)

Question (b)