Question

y^{2}-9y - 36

Explanation:

Step1: Factor - find two numbers

We need two numbers that multiply to - 36 and add up to - 9. The numbers are - 12 and 3 since $(-12)\times3=-36$ and $-12 + 3=-9$.

Step2: Rewrite the expression

$y^{2}-9y - 36=y^{2}-12y+3y - 36$.

Step3: Group and factor by grouping

Group the terms: $(y^{2}-12y)+(3y - 36)$. Factor out the greatest - common factor from each group. From the first group, we can factor out $y$: $y(y - 12)$. From the second group, we can factor out 3: $3(y - 12)$.

Step4: Combine the factors

Then $y(y - 12)+3(y - 12)=(y - 12)(y + 3)$.

Answer:

$(y - 12)(y + 3)$