Answer:
The number which should be added with 49x square + 4y square to get a perfect square is 28xy
Step-by-step 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: [tex]49x^2+4y^2[/tex]
For the expression to be perfect square it should be of form: [tex]a^2+2ab+b^2=(a+b)^2[/tex]
Now, we are given [tex]49x^2+4y^2[/tex] and we need to find the middle term
So, solving:
[tex]49x^2+4y^2\\=(7x)^2+(2y)^2+2(7x)(2y)-2(7x)(2y)\\=7x^2+28xy+(2y)^2-28xy\\=(7x+2y)^2-28xy[/tex]
The number which should be added with 49x square + 4y square ([tex]49x^2+4y^2[/tex]) to get a perfect square is 28xy
