Expanding both sides:
Left side:(x^2 + 9x + 61)(x^2 + 9x + 61)= x^4 + 9x^3 + 61x^2 + 9x^3 + 81x^2 + 549x + 61x^2 + 549x + 3721= x^4 + 18x^3 + 191x^2 + 1098x + 3721
Right side:(x^2 + 3x - 25)(x^2 + 3x - 25)= x^4 + 3x^3 - 25x^2 + 3x^3 + 9x^2 - 75x - 25x^2 - 75x + 625= x^4 + 6x^3 - 91x^2 - 150x + 625
Therefore, the equation (x^2+9x+61)^2 = (x^2+3x-25)^2 is not true for all values of x.
Expanding both sides:
Left side:
(x^2 + 9x + 61)(x^2 + 9x + 61)
= x^4 + 9x^3 + 61x^2 + 9x^3 + 81x^2 + 549x + 61x^2 + 549x + 3721
= x^4 + 18x^3 + 191x^2 + 1098x + 3721
Right side:
(x^2 + 3x - 25)(x^2 + 3x - 25)
= x^4 + 3x^3 - 25x^2 + 3x^3 + 9x^2 - 75x - 25x^2 - 75x + 625
= x^4 + 6x^3 - 91x^2 - 150x + 625
Therefore, the equation (x^2+9x+61)^2 = (x^2+3x-25)^2 is not true for all values of x.