Factorise a2 - b2. Hence find the exact values 6782 - 782.

Here are the solutions to the problems.

12. Factorise $a^2 - b^2$. Hence find the exact values $678^2 - 78^2$.

Step 1: Factorise $a^2 - b^2$.
This is a difference of squares, which factors as:

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

Step 2: Apply the factorization to $678^2 - 78^2$.
Substitute $a = 678$ and $b = 78$ into the factored form:

$$$$