Factorise by grouping in pairs: ax + ay + 3bx + 3by and 7a + 14b + ax + 2bx

Here are the factorisations by grouping in pairs:

1. $ax + ay + 3bx + 3by$

Step 1: Group the terms.

$$(ax + ay) + (3bx + 3by)$$

Step 2: Factor out the common factor from each group.

$$a(x+y) + 3b(x+y)$$

Step 3: Factor out the common binomial $(x+y)$.

$$\boxed{(a+3b)(x+y)}$$

2. $7a + 14b + ax + 2bx$

Step 1: Group the terms.

$$(7a + 14b) + (ax + 2bx)$$

Step 2: Factor out the common factor from each group.

$$$$