Hopefully, you understand that expanding a quadratic means to remove the brackets.

It is more common however to see factorising quadratic questions in a maths exam.

**Factorising **is simply the opposite of expanding, you are simply **putting a quadratic into brackets**.

**What does factorising look like?**

When you factorise a quadratic, the answer will normally be in two brackets.

x^{2} + ax + b = (x + c) (x + d) {where a,b,c and d are integers}

All we have to be able to do is say what the numbers in the brackets (c and d) are for any given values of a and b.

**How to use the grid method to factorise**

We know that when we expand a bracket, we multiply out the terms. This means that we can use a multiplication grid to factorise.

**Example:**

Factorise x^{2 }+ 7x + 10 into the form (x + a)(x + b)

**Step 1: Start by drawing a 2 x 2 multiplication grid and inserting the first and last terms of the quadratic.**

**Step 2:** **Find what must go into the other two cells.**

These terms have to **add **to the middle term in the quadratic (7x)

and **multiply** to the product of the two numbers we have already put into the grid (10x^{2}).

The only two terms that satisfy this are 5x and 2x. (5x + 2x = 7x and 5x x 2x = 10x^{2})

**Step 3: Factorise each row and column.**

**Step 4: Put together the grid.**

**Step 5**:** Create the brackets from the grid.**

The two brackets are given by the terms in red.

So x^{2 }+ 7x + 10 ≡ (x + 5)(x + 2)

This could also be written the other way round

x^{2 }+ 7x + 10 ≡ (x + 2)(x + 5)

You can quite happily just swap these brackets round (but not the numbers inside them)

**This seems very long winded and time consuming!**

You will probably have seen quicker methods than this for factorising quadratics, however this method will work for **every** quadratic factorisation. It works for quadratics with negatives as well as quadratics such as 6x^{2} + 7x + 2 and even 2x^{2} + 3xy + 2y^{2}. It’s definitely worth learning!

Let's try some questions.