From factorising a^2-b^2 hence or otherwise simplify fully (x^2 + 4)^2 - (x^2-2)^2

This question is a GCSE Higher tier style question. First the student should recognise that a²-b²= (a-b)(a+b). Using this to solve (x²+4)²-(x²-2)² - Where a = (x²+4) and b = (x²-2). Therefore substituting a and b into (a-b)(a+b)...(x²+4+x²-2)(x²+4-x²+2) and simplifying...(2x²+2)(6). Expanding out the brackets gives: 12x²+12. Factorising out the 12 gives you 12(x²+1). The final answer!