NECO 2023 · Paper 1 · Q28

What must be added to $2y^2 + 7y$ to make it a perfect square?

Worked solution (try it first)

Take out the 2 so the $y^2$ term has coefficient 1: $2y^2 + 7y = 2\left(y^2 + \frac72y\right)$ .
Inside the bracket, add the square of half of $\frac72$ : $\left(\frac74\right)^2 = \frac{49}{16}$ .
Outside the bracket that is $2 \times \frac{49}{16} = \frac{49}{8}$ .
So add $\frac{49}{8}$ , option D.