Factorise the following expressions: 1.1 2x + 4y - 6z 1.2 10p6q2 - 4p3q2 + 2p4q4 1.3 (m+n)2 - 5p(m+n) 1.4 4(7c - d) + a(d - 7c) 1.5 3ax - 6bx + 6ay - 12by

The GCF of $2, 4,$ and 6 is 2.

$$2x + 4y - 6z = 2(x) + 2(2y) - 2(3z)$$ $$= 2(x + 2y - 3z)$$

The factorised expression is $\boxed{2(x + 2y - 3z)}$.

The GCF of the coefficients $10, 4,$ and 2 is 2.
The GCF of the $p$ terms ($p^6, p^3, p^4$) is $p^3$.
The GCF of the $q$ terms ($q^2, q^2, q^4$) is $q^2$.
So, the overall GCF is $2p^3q^2$.

$$10p^6q^2 - 4p^3q^2 + 2p^4q^4 = 2p^3q^2(5p^3) - 2p^3q^2(2) + 2p^3q^2(p q^2)$$ $$= 2p^3q^2(5p^3 - 2 + p q^2)$$

The factorised expression is $\boxed{2p^3q^2(5p^3 - 2 + p q^2)}$.

$$(m+n)^2 - 5p(m+n) = (m+n)(m+n) - 5p(m+n)$$ $$= (m+n)[(m+n) - 5p]$$ $$= (m+n)(m+n - 5p)$$

The factorised expression is $\boxed{(m+n)(m+n - 5p)}$.

Note that $(d - 7c) = -(7c - d)$.

$$4(7c - d) + a(d - 7c) = 4(7c - d) + a[-(7c - d)]$$ $$= 4(7c - d) - a(7c - d)$$

$$= (7c - d)(4 - a)$$

The factorised expression is $\boxed{(7c - d)(4 - a)}$.

$$(3ax - 6bx) + (6ay - 12by)$$

Factor $3x$ from the first pair and $6y$ from the second pair.

$$3x(a - 2b) + 6y(a - 2b)$$

The GCF of $3x$ and $6y$ is 3.

$$(a - 2b)3(x + 2y)$$ $$= 3(a - 2b)(x + 2y)$$

The factorised expression is $\boxed{3(a - 2b)(x + 2y)}$.