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 $ax^2+bx+c$.

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.

Note that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.

Part of HELM Book 1.3

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

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Basic Algebra question, expand one set of brackets, coefficients may be positive or negative, pronumerals randomised.

Quiz for expanding brackets and factorising

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

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

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

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

9 questions: Expanding out expressions such  $(ax+b)(cx+d)$ etc.

Simple multiplication of complex conjugates. Complex numbers are of the form $a+bi$ where $a$ and $b$ are randomised between 1 and 9 inclusive. 

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Expand $(ay+b)(cy+d)(py+q)$.

Includes a video expanding three brackets, however uses the variable $x$ rather than $y$.

Expand $ax(cx+d)$ and expand $(rx+s)(px)$

Expand $(ax+b)(cx+d)$.

Expand $(pw+q)(aw^2+bw+c)$.

Expand $(az^2+bz+c)(pz+q)$.

Expand $(az^2+bz+c)(dz^2+pz+q)$.

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Solve $\displaystyle ax + b =\frac{f}{g}( cx + d)$ for $x$.

A video is included in Show steps which goes through a similar example.