Simplify the expression: $$y^2 - 14y + 49 - (y-8)^2$$

Solution:

• Expand the squared terms:
  • \((y-8)^2 = y^2 - 16y + 64\)
• Substitute and simplify:
  • \(y^2 - 14y + 49 - (y^2 - 16y + 64)\)
  • \(y^2 - 14y + 49 - y^2 + 16y - 64\)
  • \((y^2 - y^2) + (-14y + 16y) + (49 - 64)\)
  • \(0 + 2y - 15\)
  • \(2y - 15\)

Answer: $$2y - 15$$