Question

If A is 25 x square+64 y square then the term to be added to A to make it a perfect square is​

Answer 1

A = 25x² + 64y² = (5x)² + (8y)²

(5x+8y)² = 25x² + 64y² + 80xy

So, 80xy should be added to A to make it a perfect square.

Answer 2

$wkt \\ \\ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ now \\ \\ A = 25 {x}^{2} + 64 {y}^{2} \\ \\ A = {(5x)}^{2} + {(8y)}^{2} \\ \\ A + 2(5x)(8y) = {(5x)}^{2} + {(8y)}^{2} + 2(5x)(8y) \\ \\ A + 2(5x)(8y) = {(5x + 8y)}^{2}$

Therefore 80xy must be added to A to make it a perfect square.

hope it helps