Expand and simplify (x-2)(2x+3)(x+1)

When answering this type of question, it is often easiest to break working out down into two big chunks, to keep everything organised.

Chunk One - Expanding and Simplifying Two of the Brackets

To begin, you should select two of the three brackets to expand: for this example, we will use (2x + 3)(x + 1) and the FOIL method of expansion to multiply all of the terms.



First - take the first terms of the brackets (so 2x and x) and multiply them together: for this example that gives 2x2 

Outside - take the two outermost terms of the brackets (2x and 1) and multiply them together: for this example that gives 2x

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 1) and multiply them together: for this example that gives 3.

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
2x2 + 2x + 3x + 3

Then, we will simplify this expression by grouping any “like” terms (this just means group together any bits with x where they have the same power)                     
2x2 + 5x + 3

Chunk Two: Multiplying the final bracket by your simplified expression

The easiest way to do this next step is to use a table, and multiply your algebraic terms together in the same way you would using a grid method for long multiplication.

To begin, draw a grid and label it as shown below. Along the top of the grid, you should have the terms from your simplified expression, and down the side you should have the terms of the final bracket.



Next, fill in the grid by multiplying the terms (e.g. to fill in the first box you would do 2x2 multiplied by x, leaving us with 2x3) and take extra care to watch out for any negative terms when multiplying.

Your completed table should look like the diagram below:



Next, you need to group together any like terms and write the simplified expression by finding any x terms which have the same powers.



Doing this leaves you with your final answer, which ends up being 2x3 + x2 - 7x - 6.