1. **Factorise the expression 9p^2 - q^2** This is a difference of squares, which follows the formula: $$a^2 - b^2 = (a - b)(a + b)$$ Here, $a = 3p$ and $b = q$. So, $$9p^2 - q^2 = (3p - q)(3p + q)$$ 2. **Check the equation (c + 2d)^2 = (c + 2d)(3c - 7d)** First, expand the left side: $$(c + 2d)^2 = (c + 2d)(c + 2d) = c^2 + 4cd + 4d^2$$ Now, expand the right side: $$(c + 2d)(3c - 7d) = 3c^2 - 7cd + 6cd - 14d^2 = 3c^2 - cd - 14d^2$$ Since the two sides are not equal, the given equation is incorrect as stated. 3. **Factorise 32a^2 - 98b^2** First, factor out the greatest common factor (GCF): $$2(16a^2 - 49b^2)$$ Notice $16a^2 - 49b^2$ is a difference of squares: $$16a^2 - 49b^2 = (4a)^2 - (7b)^2 = (4a - 7b)(4a + 7b)$$ So the full factorisation is: $$2(4a - 7b)(4a + 7b)$$ **Final answers for Q1:** - a) $$(3p - q)(3p + q)$$ - b) The equation is not true as given. - c) $$2(4a - 7b)(4a + 7b)$$