Factorise the following expressions: 2.1 4x2 - 9c6 2.2 -7a2b + 28b 2.3 n4 - 1 2.4 (2x - 1)2 - 49

Here, $a = \sqrt{4x^2} = 2x$ and $b = \sqrt{9c^6} = 3c^3$.

$$4x^2 - 9c^6 = (2x)^2 - (3c^3)^2$$ $$= (2x - 3c^3)(2x + 3c^3)$$

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

The GCF of $-7$ and 28 is 7. The GCF of $a^2b$ and $b$ is $b$.
So, the common factor is $7b$. We can factor out $-7b$ to make the leading term positive.

$$-7a^2b + 28b = -7b(a^2) + (-7b)(-4)$$ $$= -7b(a^2 - 4)$$

Here, $a = a$ and $b = \sqrt{4} = 2$.

$$= -7b(a - 2)(a + 2)$$

The factorised expression is $\boxed{-7b(a - 2)(a + 2)}$.

Here, $a = \sqrt{n^4} = n^2$ and $b = \sqrt{1} = 1$.

$$n^4 - 1 = (n^2)^2 - (1)^2$$ $$= (n^2 - 1)(n^2 + 1)$$

Here, $a = \sqrt{n^2} = n$ and $b = \sqrt{1} = 1$.

$$= (n - 1)(n + 1)(n^2 + 1)$$

The factorised expression is $\boxed{(n - 1)(n + 1)(n^2 + 1)}$.

Here, $a = (2x - 1)$ and $b = \sqrt{49} = 7$.

$$(2x - 1)^2 - 49 = [(2x - 1) - 7][(2x - 1) + 7]$$

$$= (2x - 1 - 7)(2x - 1 + 7)$$ $$= (2x - 8)(2x + 6)$$

From $(2x - 8)$, the GCF is 2. So, $2(x - 4)$.
From $(2x + 6)$, the GCF is 2. So, $2(x + 3)$.

$$= 2(x - 4) \cdot 2(x + 3)$$ $$= 4(x - 4)(x + 3)$$

The factorised expression is $\boxed{4(x - 4)(x + 3)}$.