Algebra

Simplify $5x + 3x - 2x$.

Simplify $5a + 3b + 2a - b$.

Expand $3(x + 4)$.

Expand $-2(x - 5)$.

Factorise $6x + 9$.

Factorise $4x^2 + 6x$.

Simplify $(4x)^2$.

Simplify $\sqrt{12}$.

Find the value of $3x + 2y$ when $x = 4$ and $y = 5$.

Solve $3x + 5 = 17$.

Expand $(x + 3)(x + 5)$.

Expand $(x - 4)(x + 3)$.

Expand $(x + 5)^2$.

Expand $(x + 6)(x - 6)$.

Factorise $x^2 + 7x + 12$.

Factorise $x^2 + 3x - 10$.

Simplify $\sqrt{6} \times \sqrt{24}$.

Simplify $\sqrt{8} + \sqrt{18}$.

Solve $3(x - 4) = 9$.

When $a = 3$ and $b = -2$, find the value of $a^2 - 3ab + 2b$.

Factorise $x^2 - 49$.

Factorise $2x^2 + 7x + 3$.

Simplify $(3 + \sqrt{5})(3 - \sqrt{5})$.

Rationalise the denominator of $\dfrac{6}{\sqrt{3}}$.

Solve the system: $\begin{cases} y = 2x + 1 \\ y = -x + 7 \end{cases}$

Solve the system: $\begin{cases} 2x + 3y = 15 \\ 2x + 1y = 9 \end{cases}$

Factorise fully $2x^2 - 18$.

Solve $\dfrac{x + 3}{4} = 5$.

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

The sum of two numbers is $30$ and their difference is $6$. Find both numbers.

Solve the system: $\begin{cases} 3x + 2y = 12 \\ 2x - 5y = -11 \end{cases}$

Factorise fully $6x^2 - 5x - 4$.

Rationalise the denominator of $\dfrac{2}{3 + \sqrt{5}}$.

If $x + \dfrac{1}{x} = 3$ (with $x > 0$), find $x^2 + \dfrac{1}{x^2}$.

A cinema sells adult tickets at £$12$ and child tickets at £$8$. One evening it sold $80$ tickets for £$832$. How many adult and child tickets were sold?

Solve $x^2 + 7x + 12 = 0$.

Simplify $\dfrac{x^2 - 25}{x + 5}$.

Solve simultaneously: $y = x^2$ and $y = 3x + 4$.

Simplify $(\sqrt{3} + \sqrt{12})^2$.

Find $x$ such that $x^2 = 50$, giving exact answers in surd form.