(a) Factorise the following expressions: (1) \( m x+m y+n x+n y \) (3) \( 3 a p-3 b p-3 a q+3 b q \) (5) \( 2 x^{3}-8 x y^{2}+x^{2} y-4 y^{3} \) (7) \( p x^{3}+p+x^{3}+1 \) (9) \( x y+3 a+3 y+a x \) (11) \( a^{2} x+y-x-a^{2} y \)

To factorise those expressions, let's break them down. 1. \( mx + my + nx + ny \) can be grouped as \( (mx + nx) + (my + ny) = (m+n)(x+y) \). 3. \( 3ap - 3bp - 3aq + 3bq \) can be factored as \( 3p(a-b) + 3q(b-a) = 3(a-b)(p-q) \). 5. For \( 2x^3 - 8xy^2 + x^2y - 4y^3 \), we can factor out a 2 to get \( 2(x^3 - 4xy^2 + \frac{1}{2}x^2y - 2y^3) \). Rearranging terms allows us to factor by grouping, leading to \( 2(x-y)(x^2 + 2xy + 2y^2) \). 7. The expression \( px^3 + p + x^3 + 1 \) can be rewritten as \( p(1 + x^3) + (1 + x^3) = (1 + x^3)(p + 1) \) for the factorization. 9. For \( xy + 3a + 3y + ax \), rearranging gives \( xy + ax + 3a + 3y = y(x + 3) + 3(a + y) \), so we factor as \( (x + 3)(y + a) \). 11. The last expression \( a^2x + y - x - a^2y \) can be regrouped: \( a^2x - x + y - a^2y = x(a^2 - 1) + y(1 - a^2) = (a^2 - 1)(x - y) \). Happy factorising!