Algebra Toolkit Practice Questions

Factorise fully $10a^3b - 15a^2b^2$

Factorise $25p^2 - 4q^2$

Factorise fully $x^4 - 36x^2$

Expand and simplify $(2x - 3)(x + 5) - x(x - 4)$

Write $x^2 - 14x + 5$ in the form $(x + a)^2 + b$, where $a$ and $b$ are integers.

Hence write down the minimum value of $x^2 - 14x + 5$ and the value of $x$ at which it occurs.

Expand and simplify fully $(2x - 1)(x + 3)(4 - x)$

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

Write $3x^2 - 12x + 5$ in the form $a(x + b)^2 + c$, where $a$, $b$ and $c$ are integers.

Hence solve $3x^2 - 12x + 5 = 0$, giving your answers in surd form.

Work out the values of $c$, $d$ and $n$.

Factorise $10x^2 - 29x + 21$

Factorise $12x^2 + 7xy - 12y^2$

Show that $2x^2 - 5x - 42 = 0$

Work out the perimeter of the rectangle.

Solve $(x + 4)(x - 2) = 3x(x - 1) - 11$

Do not use trial and improvement.

You must show your working.

Factorise fully $(3x + 4)^2 - (x - 6)^2$

Write $7 + 12x - 2x^2$ in the form $p - q(x + r)^2$, where $p$, $q$ and $r$ are integers.

Hence write down the maximum value of $7 + 12x - 2x^2$ and the value of $x$ at which this maximum occurs.

Express $r$ in terms of $a$.