Expand and simplify (x+3)(x+5)

The easiest method for expanding these brackets is to use the FOIL method of expansion.
This ensures you multiply every aspect of the brackets together.



First - take the first terms of the brackets (so, x and x) and multiply them together: for this example that gives x2.

Outside - take the two outermost terms of the brackets (x and 5) and multiply them together: for this example that gives 5x.

Inside - take the two innermost terms of the brackets (3 and x) and multiply them together: for this example that gives 3x.

Last - take the last terms of the brackets (so 3 and 5) and multiply them together: for this example that gives 15.

Some people may draw lines between terms when doing this (as seen in the diagram above) leaving you with a “crab claw” around the brackets.

Write down everything you have worked out as one long expression:
x2 + 5x + 3x + 15

Then, we will simplify this expression by grouping any “like” terms (this just means adding together any bits with x where they have the same power).

This leaves us with our final answer, which is:           
x2 + 8x + 15