what must be the value of c to make 25x^2-30xy+c a perfect square trinomial?

To make the expression 25x^2 - 30xy + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be factored into the square of a binomial. In this case, the square of a binomial would have the form (Ax + By)^2, where A and B are constants.

Let's expand the square of a binomial to find the value of c:
(Ax + By)^2 = (Ax)^2 + 2(Ax)(By) + (By)^2
= A^2x^2 + 2ABxy + B^2y^2

Comparing this expanded form with the given expression, 25x^2 - 30xy + c, we can determine the values of A, B, and c.

A^2x^2 = 25x^2, which means A^2 = 25.
Taking the square root of both sides, we get A = ±5.

2ABxy = -30xy, which means AB = -15.

B^2y^2 = 0y^2, which means B^2 = 0.
Since B^2 = 0, B must be equal to 0.

So, we have A = ±5, B = 0, and c = B^2y^2 = 0.

Thus, to make the expression 25x^2 - 30xy + c a perfect square trinomial, the value of c must be 0.

if it is (5x-a)^2 then that is

25x^2 - 10ax + a^2
so a=3 and c=9