1. **Problem Statement:** We have a rectangular garden with dimensions $(2x + 3)$ metres and $(x - 1)$ metres. 2. **Write an expression for the area:** The area $A$ of a rectangle is given by the formula: $$A = \text{length} \times \text{width}$$ Here, length = $2x + 3$ and width = $x - 1$. So, $$A = (2x + 3)(x - 1)$$ 3. **Expand the expression:** Use the distributive property (FOIL method): $$A = 2x \times x + 2x \times (-1) + 3 \times x + 3 \times (-1)$$ $$A = 2x^2 - 2x + 3x - 3$$ Simplify like terms: $$A = 2x^2 + x - 3$$ 4. **Calculate the area when $x = 5$:** Substitute $x = 5$ into the expanded expression: $$A = 2(5)^2 + (5) - 3 = 2(25) + 5 - 3 = 50 + 5 - 3 = 52$$ So, the area is 52 square metres. 5. **Factorise the expanded expression:** We want to factorise: $$2x^2 + x - 3$$ Find two numbers that multiply to $2 \times (-3) = -6$ and add to $1$ (the coefficient of $x$). These numbers are 3 and -2. Rewrite the middle term: $$2x^2 + 3x - 2x - 3$$ Group terms: $$(2x^2 + 3x) - (2x + 3)$$ Factor each group: $$x(2x + 3) - 1(2x + 3)$$ Factor out common binomial: $$(2x + 3)(x - 1)$$ 6. **Verification:** The factorised form matches the original expression for the area. **Final answers:** - a) Area expression: $A = (2x + 3)(x - 1)$ - b) Expanded: $A = 2x^2 + x - 3$ - c) Area at $x=5$: $52$ square metres - d) Factorised: $A = (2x + 3)(x - 1)$