Simplifying algebraic expressions

Determine expressions for internal shear and bending moment as a function of $x$ for a beam with two vertical loads.

This shows how to take an expression given by the student and plot the implicit curve of points where it equals zero.

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Part 1: multiply a 3D vector by an integer scalar
Part 2: perform scalar multiplication and subtraction in one expression with two 3D vectors

This question asks the student to give a function with a particular root. It then asks them to divide by (x-{root}), and uses adaptive marking to mark against the previous answer.

This uses the "expression" data type, which is currently undocumented and experimental.

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

Simplifying expressions from $\frac{x^mx^n}{x^p}$ to $x^{m+n-p}$. 

Used in a LANTITE workshop.

Filling in the blanks from the answer to a simplified expression involving indices.

Simplifying expressions from $\frac{x^mx^n}{x^p}$ to $x^{m+n-p}$. 

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

Shows two different ways

Collecting like terms, expanding a bracket (distributive law), substitution of values, finding factors, simplifying algebraic fractions.

Shows how to mark a boolean expression, by checking all possible values of the free variables. There's an information step containing a reminder of the syntax for boolean operations.

If possible, simplify simple expressions by collecting like terms.

Rewriting a trigonometric expression of the form $A\cos(\theta)\pm B\sin(\theta)$ to either $R\sin(\theta+\alpha)$ or $R\cos(\theta+\alpha)$ by calculating $R$ and $\alpha$. 

Rewriting a trigonometric expression of the form $A\sin(\theta)-B\cos(\theta)$ to $R\sin(\theta-\alpha)$ by calculating $R$ and $\alpha$.

Differentiate a polynomial expression involving coefficients and, negative and fractional indices. 

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

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

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

Simplifying first is essential in terms of managing expressions that might need factorising.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Substitute values into an algebraic expression and calculate the result.

Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$.

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Using indices rules to rewrite an expression from $a^\frac{m}{n}$ to $b$, for integers $a$, $b$, $m$ and $n$.

Simplifying algebraic expressions