Question: 

Expand (2x-3)(4x+4) 

We will be using the FOIL method. FOIL is an ancronym: 

F=first

O=outside

I=inside

L=last

So, to begin, we start with the first term in each bracket, and multiply them together. 

2x*4x=8x²

Next, we take the outside terms of the brackets, so 2x and 4.

2x*4=8x

Now, we move onto the inside terms. Now this may seem a little complicated. As the first bracket is (2x-3), we must always involve the fact that the 3 is negative. So, we are using the figures, -3 and 4x

-3*4x=-12x

Finally, the last terms 

-3*4=-12

We then add all these answers up

8x²+8x-12x-12=

8x²-4x-12

Therefore (2x-3)(4x+4)=8x²-4x-12