1. **Problem statement:** Factorise each of the following expressions completely. 2. **Recall the factoring rule:** To factorise an expression, find the greatest common factor (GCF) of all terms and factor it out. 3. **(a) Factorise $12r - 9$:** - Find GCF of 12 and 9, which is 3. - Factor out 3: $$12r - 9 = 3(\cancel{4}r - \cancel{3})$$ - So, the factorised form is $3(4r - 3)$. 4. **(b) Factorise $-25y - 35$:** - Find GCF of 25 and 35, which is 5. - Note the negative sign; factor out $-5$ to keep the expression positive inside parentheses: $$-25y - 35 = -5(\cancel{5}y + \cancel{7})$$ - So, the factorised form is $-5(5y + 7)$. 5. **(c) Factorise $27b - 36by$:** - Find GCF of 27 and 36, which is 9. - Both terms have $b$. - Factor out $9b$: $$27b - 36by = 9b(\cancel{3} - \cancel{4}y)$$ - So, the factorised form is $9b(3 - 4y)$. 6. **(d) Factorise $8ax + 12a - 4az$:** - Find GCF of 8, 12, and 4, which is 4. - All terms have $a$. - Factor out $4a$: $$8ax + 12a - 4az = 4a(\cancel{2}x + \cancel{3} - \cancel{1}z)$$ - So, the factorised form is $4a(2x + 3 - z)$. 7. **(e) Factorise $4m - 6my - 18mz$:** - Find GCF of 4, 6, and 18, which is 2. - All terms have $m$. - Factor out $2m$: $$4m - 6my - 18mz = 2m(\cancel{2} - \cancel{3}y - \cancel{9}z)$$ - So, the factorised form is $2m(2 - 3y - 9z)$. **Final answers:** (a) $3(4r - 3)$ (b) $-5(5y + 7)$ (c) $9b(3 - 4y)$ (d) $4a(2x + 3 - z)$ (e) $2m(2 - 3y - 9z)$