Ben McGovern

Multiplying a linear expression of the form $mx+c$ by a quadratic expression of the form $ax^2+bx+c$. 

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$.

Factorise a cubic expression into the product of three linear factors of the form $mx+c$, where one of the factors is given. 

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

Factorising a quadratic expression of the form $ax^2+bx+c$, where $a>1$.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression of the form $x^2+bx+c$ by completing the square.

Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{x+a}$ as partial fractions in the form $\frac{A}{x+a}+Bx+C$.

Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+C$.

Rewrite the expression $\frac{mx+a}{nx+b}$ as partial fractions in the form $A+\frac{B}{nx+b}$.

Rewrite the expression $\frac{x+a}{x+b}$ as partial fractions in the form $A+\frac{B}{x+b}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{n}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{cx+d}{(kx+a)(x+b)}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{n}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{n}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{cx+d}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{c}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

Rewrite the expression $\frac{c}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{c}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{c}{(kx+a)(x+b)}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$.

Simplifying an expression of the form $\frac{a^4b^3}{\sqrt{a^4b^2}}$ to $a^2b^2$, for integers $a$ and $b$.