The problem asks to factorise the given expressions completely. We have two parts: (a) $8x^2(x-7) - 10x(x-7) - 3(x-7)$ (b) $4x^3$ (This part of the question is not addressed, as it is incomplete. There is a missing expression.)

1. Problem Description

The problem asks to factorise the given expressions completely. We have two parts:

(a) $8x^2(x-7) - 10x(x-7) - 3(x-7)$

(b) $4x^3$ (This part of the question is not addressed, as it is incomplete. There is a missing expression.)

2. Solution Steps

(a) $8x^2(x-7) - 10x(x-7) - 3(x-7)$

Notice that the term $(x-7)$ is common to all the terms. We can factor this out.

$(x-7)(8x^2 - 10x - 3)$

Now we need to factorise the quadratic expression $8x^2 - 10x - 3$. We are looking for two numbers that multiply to $8 * -3 = -24$ and add up to $-10$. These two numbers are $-12$ and $2$. So we can split the middle term as follows:

$8x^2 - 12x + 2x - 3$

Now we factor by grouping.

$4x(2x - 3) + 1(2x - 3)$

$(4x+1)(2x-3)$

Putting it all together, we have:

$(x-7)(4x+1)(2x-3)$

3. Final Answer

(a) $(x-7)(4x+1)(2x-3)$

(b) Cannot be solved as information is not complete.