Question

1. $y^2 + 9y + 8$

Explanation:

Step1: Find two numbers that multiply to 8 and add to 9.

The numbers are 1 and 8 since \(1\times8 = 8\) and \(1 + 8=9\).

Step2: Factor the quadratic expression.

Using the numbers from Step 1, we can factor \(y^{2}+9y + 8\) as \((y + 1)(y + 8)\) because when we expand \((y + 1)(y + 8)\) using the distributive property (FOIL method), we get \(y^{2}+8y+y + 8=y^{2}+9y + 8\).

Answer:

\((y + 1)(y + 8)\)