Question

What is the number which is to be added with 49x square + 4y square to get a perfect square

Answer 1

The number which should be added with 49x square + 4y square to get a perfect square is 28xy

Explanation:

We need to find the number which is to be added with 49x square + 4y square to get a perfect square.

The expression given is:
`49x^2+4y^2`

For the expression to be perfect square it should be of form:
`a^2+2ab+b^2=(a+b)^2`

Now, we are given
`49x^2+4y^2` and we need to find the middle term

So, solving:

`49x^2+4y^2\\=(7x)^2+(2y)^2+2(7x)(2y)-2(7x)(2y)\\=7x^2+28xy+(2y)^2-28xy\\=(7x+2y)^2-28xy`

The number which should be added with 49x square + 4y square (
`49x^2+4y^2`) to get a perfect square is 28xy