Binomial Expansion (Edexcel IAL Maths): Exam Questions

Evaluate

(i) $4!$

(ii) ${}^{5}C_{2}$

(iii) ${}^{6}C_{3}$

Show that, for all values of $k$,

$C pre^{k}_{1} = k$

Expand $(x+2)^{4}.$

Find the first three terms, in ascending powers of $x$, in the expansion of $(3+2x)^{8}$.

Find the coefficient of the $x^{2}$ term in the expansion of $(2-x)^{5}$.

Expand .$(2x-3)^{6}$.

In the expansion of $(p+x)^{12}$, the coefficient of the $x^{5}$ term is 12 976 128. Find the value of $p$.

Find the first three terms in the expansion of $(5+2x)^{5}$.

Use your answer to part (a) to estimate the value of $(5.04)^{5}$.

In the expansion of $(p+x)^{4}$, where $p$ is a non-zero constant, the coefficient of the $x^{2}$ term is twice the coefficient of the $x$ term. Find the value of $p$.

Expand $(2+x)^{4}.$

Find the coefficient of the term in $x^{3}$ in the expansion of $(2-x)^{8}$.

Find the first three terms, in ascending powers of $x$, in the expansion of $(3+x)^{4}$.

Use your answer to part (a) to estimate $(3.1)^{4}$.

In the expansion of $(a-x)^{4}$, the coefficient of the $x^{2}$ term is 96. Given that $a>0$, find the value of $a$.

Find the first three terms in the expansion of $(9-2x)^{5}$.

Use your answer to part (a) to estimate $(8.9)^{5}$.

In the expansion of $(a-2x)^{5}$, the coefficient of the $x^{2}$ term is equal to the coefficient of the $x^{3}$ term. Find the value of $a$.

In the expansion of $(3+px)^{6}$, the coefficient of the $x^{4}$ term is four times the coefficient of the $x^{2}$ term. Find the possible values of $p$.

Find the first three terms in the expansion of $(3+2x)^{8}$.

Given that $x$ is small such that $x^{3}$and higher powers of $x$ can be ignored show that

$(1+x)(3+2x)^{8}\approx6561+41553x+116640x^{2}$

In the expansion of $(p+qx)^{5}$, the coefficients of the $x^{2}$ term and the $x^{3}$ term are equal.

Find $p$ in terms of $q$.

In the expansion of $(a+bx)^{4}$, the coefficient of the $x^{2}$ term is equal to the coefficient of the $x^{3}$ term.

Show that $\frac{a}{b}=\frac{2}{3}$.

Given that $a$ and $b$ are integers, and that $10<b<15$, find the values of $a$ and $b$.

Fully expand $(4-x)^{4}$.

Fully expand $(2-\frac{1}{3}x)^{4}$.

Find the coefficient of the term in $x^{4}$ in the expansion of $(3+2x)^{9}.$

Find the first three terms, in ascending powers of $x$, in the expansion of $(5-2x)^{4}.$

Use your answer to part (a) to estimate $(4.5)^{4}$.

In the expansion of $(4-px)^{6}$, the coefficient of the $x^{4}$ term is 19 440. Given that $p$ is a positive integer find the value of $p$.

In the expansion of $(3a-2x)^{6},$ the coefficient of the $x^{3}$ term is equal to the coefficient of the $x^{4}$ term. Find the value of $a$.

Find the first three terms in the expansion of $(2-3x)^{7}$.

Given that $x$ is small such that $x^{3}$ and higher powers of $x$ can be ignored show that

$(1-2x)(2-3x)^{7}\approx128-1600x+8736x^{2}$

In the expansion of $(p+qx)^{8}$, the coefficients of the $x^{2}$ term and the $x^{6}$ term are equal.

Find $p$ in terms of $q$.

In the expansion of $(1+x)^{n},$ the coefficient of the $x^{3}$ term is 84.

Find the value of $n$.

In the expansion of $(a+bx)^{4},$ the coefficient of the $x^{3}$ term is 216.

In the expansion of $(a+bx)^{6},$ the coefficient of the $x^{4}$ term is 4860.

Find the possible values of $a$ and $b$.

Expand .$(3-2x)^{5}$

Find the coefficient of the term in $x^{4}$ in the expansion of $(4-3x)^{7}.$.

Given that ${}^{n}C_{3} = 35$ find the value of $n$.

Use the first three terms, in ascending powers of $x$, in the expansion of $(3-5x)^{4}$ to find an approximation for $(2.6)^{4}$.

Using your calculator, find the percentage error in the approximation from part (a) to the exact value of $(2.6)^{4}$.

In the expansion of $(m-\frac{1}{4}x)^{5}$, the coefficient of the $x^{3}$ term is -10. Find the possible values of $m$.

In the expansion of $(3a+\frac{1}{2}x)^{6}$, the coefficient of the $x^{3}$ term is equal to the coefficient of the $x^{5}$ term. Find the values of $a$, giving your answers in the form $\frac{\sqrt{m}}{n}$, where $m$ and $n$ are integers to be found.

Find the first three terms in the expansion of $(4-3x)^{9}$.

Given that $x$ is small such that $x^{3}$ and higher powers of $x$ can be ignored show that

$(3-2x^{2})(4-3x)^{9}\approx786432-5308416x+15400960x^{2}$

In the expansion of $(p+qx)^{9}$, the coefficient of the $x^{3}$ term is double that of the $x^{5}$ term. Find $p$ in terms of $q$.

In the expansion of $(1-3x)^{n},$ the coefficient of the $x^{3}$ term is -3240.

Find the value of $n$.

In the expansion of $(a+bx)^{8},$ the coefficient of the $x^{5}$ term is -870 912.

In the expansion of $(a+bx)^{12},$ the coefficient of the $x^{3}$ term is -1 557 135 360.

Find the possible values of $a$ and $b$.