1. **Problem 1(a): Expand and simplify** $3(2y - 5) + 7(y + 2)$ 2. Use the distributive property: multiply each term inside the parentheses by the factor outside. $$3(2y - 5) = 3 \times 2y - 3 \times 5 = 6y - 15$$ $$7(y + 2) = 7 \times y + 7 \times 2 = 7y + 14$$ 3. Add the two expressions: $$6y - 15 + 7y + 14$$ 4. Combine like terms: $$6y + 7y = 13y$$ $$-15 + 14 = -1$$ 5. Final simplified expression: $$\boxed{13y - 1}$$ 1. **Problem 1(b): Factorise fully** $6x^2 + 15x$ 2. Find the greatest common factor (GCF) of the terms: 6 and 15 have GCF 3, and both terms have at least one $x$. 3. Factor out $3x$: $$6x^2 + 15x = 3x(\cancel{\frac{6x^2}{3x}} + \cancel{\frac{15x}{3x}}) = 3x(2x + 5)$$ 4. Final factorised form: $$\boxed{3x(2x + 5)}$$ 1. **Problem 1(c): Make $g$ the subject of the formula** $f = 3g + 11$ 2. Start with the equation: $$f = 3g + 11$$ 3. Subtract 11 from both sides: $$f - 11 = 3g + \cancel{11} - \cancel{11}$$ 4. Divide both sides by 3: $$\frac{f - 11}{3} = \cancel{\frac{3g}{3}}$$ 5. Final formula with $g$ as the subject: $$\boxed{g = \frac{f - 11}{3}}$$