1. **Stating the problem:** Identify the correct expansion of the binomial expressions given. 2. **Formula used:** The binomial expansion formulas are: $$ (a - b)^2 = a^2 - 2ab + b^2 $$ $$ (a + b)^2 = a^2 + 2ab + b^2 $$ 3. **Explanation:** - Option (a) states $(a - b)^2 = a^2 + 2ab + b^2$, which is incorrect because the middle term should be negative. - Option (b) states $(a - b)^2 = a^2 - 2ab + b^2$, which is correct. - Option (c) states $(a - b)^2 = a^2 - b^2$, which is incorrect; this is the difference of squares formula for $(a - b)(a + b)$. - Option (d) states $(a + b)^2 = a^2 + 2ab + b^2$, which is correct. **Answer for question 1:** (b) and (d) are correct expansions. --- 1. **Stating the problem:** Simplify $(z^2)^3$ for a non-zero rational number $z$. 2. **Formula used:** Power of a power rule: $$ (x^m)^n = x^{m \times n} $$ 3. **Calculation:** $$ (z^2)^3 = z^{2 \times 3} = z^6 $$ **Answer for question 2:** (a) $z^6$ --- 1. **Stating the problem:** Find the surface area of a cube with volume 64 cm$^3$. 2. **Formula used:** - Volume of cube: $$ V = s^3 $$ where $s$ is side length. - Surface area of cube: $$ A = 6s^2 $$ 3. **Calculation:** - Find side length: $$ s = \sqrt[3]{64} = 4 \text{ cm} $$ - Calculate surface area: $$ A = 6 \times 4^2 = 6 \times 16 = 96 \text{ cm}^2 $$ **Answer for question 3:** (c) 96 cm$^2$