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D2. Elementary algebra : difference of two squares. Algebraic expressions like a2 - b2 or x2 -4, where both terms are perfect squares, are called the difference of two squares. Expressions like these can always be factorised. For example, x 2 - 1=( x - 1)( x + 1) or a2 - 9=(a -3 )(a + 3) Example: factorise x2 - 16 Step 1: Write down some "empty" brackets x2 - 16=  (      )(      ) Step 2: The first terms in each bracket must both be x:   (x    )(x    ) Step 3: The last terms in each bracket must multiply to give -16 and be of equal size, ie. 4 and -4   (x + 4)(x - 4) Step 4: Check that you get the correct result when you multiply out the brackets:     Use this display to check out the process: Practise factorising quadratic functions. Press the "Factorise" button to get started. x2 - = (x+ )(x- )