Question

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

`square+42x+9`

Answer 1

Using the identity,

a² + 2ab + b² = (a + b)²

We know that,

The middle term is 42x,

And last term is 9 = b²

⇒ b = 3

Thus,

2ab = 42x and b = 3:

2a × 3 = 42x

6a = 42x

∴ a = 7x

So, 

a² = (7x)²

∴ a² = 49x²

Hence, \[\boxed{49x^2}+42x+9\]