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These are the Transum resources related to the statement: "Pupils should be taught to simplify and manipulate algebraic expressions (including those involving surds {and algebraic fractions}) by: factorising quadratic expressions of the form x^{2} + bx + c, including the difference of 2 squares; {factorising quadratic expressions of the form ax^{2} + bx + c} and by simplifying expressions involving sums, products and powers, including the laws of indices".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- How old was Diophantus? An ancient riddle which can be answered by solving an equation containing fractions.
- Collecting Like Terms Practise your algebraic simplification skills with this self marking exercise.
- Algebraic Notation Simplification using the normal conventions of algebra.
- Indices A self marking exercise on indices (powers or exponents) including evaluating expressions and solving equations.
- Indices Video Indices, exponents and powers can all be used as a short way to describe repeated multiplication.
- Algebraic Fractions A mixture of algebraic fraction calculations and simplifications.
- Collecting Like Terms Video If you have forgotten what collecting like terms means watch this video for a quick refresher.

Here are some exam-style questions on this statement:

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*Multiply out and simplify:*" ... more - "
*Find the highest common factor of the following two expressions:*" ... more - "
*Simplify then find the square root of this expression:*" ... more - "
*(a) The expression \( (x+1)(2x-3)(3x+4) \) can be written in the form \(ax^3 + bx^2 + cx + d \) where \(a, b, c\) and \(d\) are integers. Find the values of \(a, b, c\) and \(d\).*" ... more - "
*Work out the exact value of \(n\).*" ... more - "
*(a) The \(n\)th term of a sequence is \(2^n+2^{n+1}\)*" ... more - "
*(a) Simplify the following expression.*" ... more - "
*(a) Without using a calculator, show that \(\sqrt{28}=2\sqrt7\)**The point \(X\) is shown on the unit grid below. The point \(Y\) is \(\sqrt17\) units from \(X\) and lies on the intersection of two grid lines. Mark one possible position for \(Y\).*" ... more - "
*If a, b and c are positive integers use the following statements to find the values of a, b and c.*" ... more - "
*Factorise the following expression*" ... more - "
*Show that:*" ... more - "
*The expression below can be written as a single fraction in the form \( \frac{a-bx}{x^2-25} \) where \(a\) and \(b\) are integers.*" ... more - "
*\(y = a \times b^{x – 2}\) where \(a\) and \(b\) are numbers.*" ... more

Here are some Advanced Starters on this statement:

**Algebraic Product**

Finding the value of the expression is easier than you think! more**Paper Ratio**

Calculate the ratio of the sides of an A4 sheet of paper without any measuring. more**Paper Surprising Perimeter**

Find the perimeter of a folded sheet of A4 paper as described in this short video. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

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