Question

Find the missing term in the following expression to make a perfect square.

`25x^2+40xy+square`

Answer 1

Using the identity,

a² + 2ab + b² = (a + b)²

We know that,

The first term is 25x² = (5x)²

⇒ a = 5x

And the middle term is 40xy = 2ab

So,

2 × 5x × b = 40xy

10x × b = 40xy

∴ b = 4y

Finding the last term,

b² = (4y)² = 16y²

∴ b² = 16y²

Hence, \[\ 25x^2+40xy+\boxed{16y^2}\]