Binomial Expansion Practice Questions

Write down the row of Pascal's triangle that gives the coefficients in the expansion of $(a + b)^6$.

Expand and simplify $(1 + 3x)^4$.

Give all terms of your expansion.

Expand and simplify $(2x - 5)^3$.

Work out the coefficient of $x^2$ in the expansion of $(2 + 5x)^6$.

You must not write out the full expansion.

Work out the coefficient of $x^3$ in the expansion of $(1 - x)(2 + 5x)^6$.

The expansions of $(2 + 5x)^3$ and $(1 + ax)^4$ have the same coefficient of $x^2$, where $a$ is a non-zero constant.

Work out the possible values of $a$.

Expand and simplify $\left(2x - \dfrac{1}{2}\right)^4$.

Give all terms of your expansion.

$n$ is a positive integer and $a$ is a non-zero constant.

The expansion of $(1 + ax)^n$ begins

$$1 + 24x + 252x^2 + \dots$$

Work out the value of $n$ and the value of $a$.