EXERCISE 12 Fully factorise each of the following expressions. 1. \( p-q-x(q-p) \) 2. \( x(a+b)-(b+a) \) 3. \( a x-b x+a y-b y-a+b \) 4. \( 3 x-6 x y-2 y+1 \) 5. \( 4 p^{3}-2 p-p q^{2}+q \) 6. \( 6 m^{2}-2 m n-3 m p+n p \) 7. \( 8 a m-10 a n-12 b m+15 b n \) 8. \( 3 x^{2}-2 x y+2 y^{2}-3 x y \) 9. \( x^{3}-x^{2} y+y^{3}-x y^{2} \) 10. \( m^{2}-9 n^{2}-3 k m+9 k n \) 1

When approaching factoring these expressions, keep in mind that understanding the structure of each expression can reveal common terms and patterns, making the process smoother. For instance, recognizing that certain groups of terms in an expression share a common factor can be your golden ticket to unlock the full factorization! Another tip is to look for special patterns like the difference of squares or perfect square trinomials that can simplify the process even further. For example, remembering that \(a^2 - b^2 = (a + b)(a - b)\) can help you factor expressions involving squared terms more quickly and accurately! Happy factoring!