Binomial Expansion (AQA GCSE Further Maths): Exam Questions

Expand and simplify fully ${\left(3+10x\right)}^4$

Expand and simplify $10{\left(4x^3+x^5\right)}^5$

The coefficient of $x^2$ in the expansion of ${\left(a+3x\right)}^5$ is 720.

Work out the value of $a$.

The coefficient of the $x^4$ term in the expansion of ${(2x+a)}^6$ is 60

Work out the possible values of $a$.

The coefficient of $x^2$ in the expansion of ${\left(1+ax\right)}^3$ is equal to the coefficient of $x^3$ in the expansion of ${\left(1-ax\right)}^4$.

Work out the non-zero value of $a$.

The sum of the coefficient of $x^2$ in the expansion of ${\left(\frac{k}{2}-x\right)}^4$ and the coefficient of $x^5$ in the expansion of ${\left(k+x\right)}^6$ is $18$.

By forming and solving an equation, find the possible values of $k$.

In the expansion of ${\left(x+\frac{2}{x^2}\right)}^6$ show that there is a constant term, and find the value of this constant.

$\left(b-x\right){\left(2+x\right)}^5\equiv 128+px+q{x}^2+...$

Find the values of constants $p$ and $q$.