Factorisation basically means to take out the common factors in a given equation.

**Example:
**Factorise the following equation

x² + 2x+ x³

The common factor in the above equation is ‘x’. So we get:

x (x + 2 + x²)

If we open the brackets, we get the original equation.

x (x + 2 + x²) = x² + 2x + x³

**Example:
**Factorise the following equation

x³ + x²y + 2x²

Here, the common factor is x². So we get:

x² (x + y + 2)

**Example:
**Factorise the following equation

2x⁴ + 4x²y + 12x³z

Here, the common factor is 2x². We get:`

2x² (x² + 2y + 6xz)

### Splitting the Middle Term

It is useful to know how to factorise quadratic equations by splitting the middle term. Here is how we do it:

You are given the quadratic equation:

2x² + 11x + 12

**Step 1:** You multiply the third term (+12) with the first term (2x²). We get:

2x² * 12 = 24x²

**Step 2:** We must split the middle term (11x) into two parts in such a way that the product of the two parts would be 24x² and their sum would be 11x.

The two parts would be: 8x and 3x.

Product of two parts = 8x * 3x = 24x²

Sum of two parts = 8x + 3x = 11x

**Step 3:** We get the following equation:

2x² + 8x + 3x + 12

**Step 4:** We factorise the first two terms and the last two terms. We get:

2x (x + 4) + 3 (x + 4)

**Step 5:** We get a common expression (x + 4) in the equation and the other expression is (2x + 3)

**Step 6:** We have factorised the equation!

(2x + 3) (x + 4)

Try multiplying the brackets and you will see that:

(2x + 3) (x + 4) = 2x² + 11x + 12