1. **Problem (a): Factorise completely** $3x(4a - 5b) - 2y(5b - 4a)$. 2. Notice that $-2y(5b - 4a)$ can be rewritten as $+2y(4a - 5b)$ because $5b - 4a = -(4a - 5b)$. 3. So the expression becomes: $$3x(4a - 5b) + 2y(4a - 5b)$$ 4. Factor out the common binomial factor $(4a - 5b)$: $$\cancel{(4a - 5b)}\left(3x + 2y\right)$$ 5. The fully factorised form is: $$ (4a - 5b)(3x + 2y) $$ --- 6. **Problem (b): Express as a single fraction in simplest form** $\frac{5y}{4} - \frac{3y + 3}{8}$. 7. Find a common denominator, which is 8. 8. Rewrite $\frac{5y}{4}$ as $\frac{10y}{8}$: $$\frac{\cancel{2} \times 5y}{\cancel{2} \times 4} = \frac{10y}{8}$$ 9. Now subtract: $$\frac{10y}{8} - \frac{3y + 3}{8} = \frac{10y - (3y + 3)}{8}$$ 10. Simplify the numerator: $$10y - 3y - 3 = 7y - 3$$ 11. Final simplified fraction: $$\frac{7y - 3}{8}$$