Algebra

Simplify $7y + 2y - 4y$.

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

Expand $5(x + 2)$.

Expand $-4(x - 3)$.

Factorise $8x + 12$.

Factorise $9x^2 + 12x$.

Simplify $(7x)^2$.

Simplify $\sqrt{18}$.

Find the value of $3x + 2y$ when $x = 6$ and $y = 3$.

Solve $4x + 2 = 18$.

Expand $(x + 4)(x + 7)$.

Expand $(x - 5)(x + 2)$.

Expand $(x + 6)^2$.

Expand $(x + 8)(x - 8)$.

Factorise $x^2 + 9x + 20$.

Factorise $x^2 + 2x - 15$.

Simplify $\sqrt{5} \times \sqrt{20}$.

Simplify $\sqrt{12} + \sqrt{27}$.

Solve $5(x - 2) = 25$.

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

Factorise $x^2 - 100$.

Factorise $3x^2 + 8x + 4$.

Simplify $(4 + \sqrt{3})(4 - \sqrt{3})$.

Rationalise the denominator of $\dfrac{10}{\sqrt{5}}$.

Solve the system: $\begin{cases} y = 3x + 2 \\ y = -x + 14 \end{cases}$

Solve the system: $\begin{cases} 3x + 4y = 26 \\ 3x + 2y = 16 \end{cases}$

Factorise fully $2x^2 - 50$.

Solve $\dfrac{x + 2}{3} = 7$.

Expand and simplify $(x + 1)(x + 6) - (x + 2)^2$.

The sum of two numbers is $50$ and their difference is $10$. Find both numbers.

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

Factorise fully $4x^2 - 4x - 3$.

Rationalise the denominator of $\dfrac{4}{5 + \sqrt{3}}$.

If $x + \dfrac{1}{x} = 4$ (with $x > 0$), find $x^2 + \dfrac{1}{x^2}$.

A cinema sells adult tickets at £$15$ and child tickets at £$10$. One evening it sold $60$ tickets for £$750$. How many adult and child tickets were sold?

Solve $x^2 + 8x + 15 = 0$.

Simplify $\dfrac{x^2 - 36}{x + 6}$.

Solve simultaneously: $y = x^2$ and $y = 5x + 6$.

Simplify $(\sqrt{2} + \sqrt{8})^2$.

Find $x$ such that $x^2 = 72$, giving exact answers in surd form.