Simplifying expressions of the form $(a_1+b_1 \sqrt{c}) - (a_2 + b_2 \sqrt{c})$.

Simplifying surds from $a\sqrt{b^2c}$ to $ab\sqrt{c}$, where $a$, $b$ and $c$ are positive integers.

Simplifying surds from $\sqrt{a^2b}$ to $a\sqrt{b}$, where $a$ and $b$ are positive integers.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Calculating a quartic polynomial by squaring a quadratic expression of the form $ax^2+bx+c$.

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 $ax^2+bx+c$.

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 $a>1$.

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 $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3

Remove the brackets from algebraic expressions. Part of HELM Book 1.3