1. **Factorise fully** $16m^7g^3 + 24m^8g^5$. Step 1: Find the greatest common factor (GCF) of the coefficients 16 and 24, which is 8. Step 2: For the variables, find the lowest powers: $m^7$ and $g^3$. Step 3: Factor out $8m^7g^3$: $$16m^7g^3 + 24m^8g^5 = 8m^7g^3(2 + 3mg^2)$$ 2. **Factorise** $y^2 - 2y - 48$. Step 1: Look for two numbers that multiply to $-48$ and add to $-2$. These are $-8$ and $6$. Step 2: Write the factorization: $$y^2 - 2y - 48 = (y - 8)(y + 6)$$ 3. **Show the inequality** $-2 \leq y < 1$ on the number line labeled from -3 to 3. This represents all values of $y$ starting from $-2$ inclusive to $1$ exclusive. 4. **Find all integer values of** $n$ such that $-3.4 < n \leq 2$. Step 1: Integers greater than $-3.4$ are $-3, -2, -1, \ldots$ Step 2: All integers less than or equal to $2$. Step 3: So $n = -3, -2, -1, 0, 1, 2$. 5. For inequality $-4 \leq 2y < 6$, with $y$ integer: Step 1: Divide the entire inequality by $2$: $$-2 \leq y < 3$$ Step 2: Since $y$ is integer, $y$ can be $-2, -1, 0, 1, 2$. 6. Solve the inequality $7l - 3 \leq 2l + 31$. Step 1: Subtract $2l$ from both sides: $$7l - 2l - 3 \leq 31$$ $$5l - 3 \leq 31$$ Step 2: Add $3$ to both sides: $$5l \leq 34$$ Step 3: Divide both sides by $5$: $$l \leq \frac{34}{5} = 6.8$$ So all $l$ such that $l \leq 6.8$ satisfy the inequality. Final answers: (a) $16m^7g^3 + 24m^8g^5 = 8m^7g^3(2 + 3mg^2)$ (b) $y^2 - 2y - 48 = (y - 8)(y + 6)$ Inequality on number line: $-2 \leq y < 1$ Values of $n$: $-3, -2, -1, 0, 1, 2$ Values of $y$: $-2, -1, 0, 1, 2$ Solution for $l$: $l \leq 6.8$