# Algebraic technique · Year 11

> Algebraic technique, Year 11: Factorising, Roots and more. Explanation, worked examples and free practice for the national curriculum in England.

In Algebraic technique (Year 11) you practise 3 skills: Factorising · Simplifying, multiplying and dividing algebraic fractions · Roots.

Factorising turns a sum into a product. Start with a common factor, then the special products, and factorise a trinomial through its roots: when the leading coefficient is not one, find two numbers whose product is the leading coefficient times the constant term and whose sum is the middle coefficient.

To add algebraic fractions, bring them to a common denominator: factorise each denominator and take the smallest product that every denominator divides. Before you simplify, factorise the numerator and the denominator, and cancel only factors, never terms. For every algebraic fraction, remember which values are not allowed: the ones that make the denominator zero.

A negative power is one over the positive power, and any number other than zero to the power of zero is one. The square root of a product is the product of the square roots, which is how you take a factor out of a root: look for a perfect square inside it.

**Tip:** After each factorisation, multiply back in your head: if you get the expression you started with, the factorisation is right.

## What you learn

### Factorising

- Example: Factorise fully: 6x + 12
- Answer: 6(x + 2)
- Solution: The common factor: 6 What is left in the bracket: x + 2 Check by expanding back to the original expression: 6(x + 2) = 6x + 12

### Simplifying, multiplying and dividing algebraic fractions

- Example: Simplify: 12x² ÷ 2x
- Answer: 6x
- Solution: Factorise the numerator: 2x × 6x ÷ 2x Cancel: 6x

### Roots

- Example: Work out: √2 × √8
- Answer: 4
- Solution: √2 × √8 = √(2 × 8) = √16 = 4

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

[Practise on the site](https://kixplo.com/uk/en/) · [All Year 11 topics](https://kixplo.com/uk/en/maths/year-11/)