Decide what number must be added to both sides of the equation to make the left side a perfect square trinomial, then factor the left s \( y^{2}-8 y=5 \) Add a number to both sides of the equation to make the left side a perfect square trinomial. \( y^{2}-8 y+16=5+16 \) (Type integers or simplified fractions.) Factor the left side of the equation and simplify the right side. \( \square^{2}=\square \) (Type integers or simplified fractions.)

To make the left side of the equation \( y^2 - 8y = 5 \) a perfect square trinomial, we need to add a specific number to both sides. 1. **Identify the number to add**: To complete the square for the expression \( y^2 - 8y \), we take half of the coefficient of \( y \) (which is -8), square it, and add it. \[ \left(\frac{-8}{2}\right)^2 = (-4)^2 = 16 \] 2. **Add this number to both sides**: \[ y^2 - 8y + 16 = 5 + 16 \] This simplifies to: \[ y^2 - 8y + 16 = 21 \] 3. **Factor the left side**: The left side \( y^2 - 8y + 16 \) can be factored as: \[ (y - 4)^2 \] 4. **Write the equation**: Now we can write the equation as: \[ (y - 4)^2 = 21 \] So, the final answers are: - The number added to both sides: **16** - The factored form of the left side: \((y - 4)^2 = 21\)