What must be added to this following to make it a perfect square y raise to power 2+12 y

Answer 1

To make the expression \( y^2 + 12y \) a perfect square, we need to complete the square.

1. Start with the given expression: \[ y^2 + 12y \]

2. To complete the square, we take the coefficient of \( y \) (which is 12), halve it, and then square it: \[ \left(\frac{12}{2}\right)^2 = 6^2 = 36 \]

3. Add and subtract this value (36) inside the expression: \[ y^2 + 12y = (y^2 + 12y + 36) - 36 \]

4. Now, rewrite the expression: \[ (y + 6)^2 - 36 \]

This shows that to make \( y^2 + 12y \) a perfect square, you need to add 36. The result is the perfect square \( (y + 6)^2 \).