The two expressions p(x)=x2+6x+9 and q(a,b)=25a2−b2 are given below.
(i) State the algebraic identities for (x+y)2 and for x2−y2.
(ii) Describe, in words, how one can recognise whether a quadratic expression is a perfect square trinomial or a difference of squares.
(iii) For each of the expressions p(x) and q(a,b), determine which of the special product patterns it matches and write the expression in its factorised form, showing clear reasoning for your choice in each case.