Factorise the following equation: 2x^2 + 8x + 8

The first step in factorising is to look for a 'common factor'. A common factor is a number or letter that all the values have in common. 

All the integers (numbers) in this equation can be divided by 2. Therefore, 2 is a common factor and we can 'take it out' of our equation as follows: 

2 (x² + 4x + 4)

Now we can focus on the equation inside the brackets. We create a frame as follows: 

(      ) (     ) 

We see that x² is the first term in our bracket. This means we can place the x's as follows:

(x   ) (x   )

Both signs in our equation are positive, which means both signs in the factorised brackets are positive:

(x +  ) (x +  )

Now is the hard part. We need to think of two numbers that will add together to get 4 and multiply together to get 4. 

The answer is 2 and 2. This gets easier with practice. We place these numbers in the brackets as follows:

(x + 2) (x + 2) 

This can also be written as: 

(x + 2)²

Our final answer is then:

2(x + 2)²

In order to check our answer is correct, we multiply the brackets out and check that our answer matches the question.