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!
