This website omits certain operational signs. As a guess, I think you meant to write negative y plus eight. Another possibility is negative y to the eighth power.
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4x + y = 10 is a perfectly valid functional form. The standard form is 4x + y - 10 = 0
y2 - 64 can be written as y2 - 82, which is of the form of a2 - b2.And a2 - b2 is factored as (a-b)(a+b).Therefore, y2 - 64 is factored as (y+8)(y-8).
y = ax^2 + bx + c
4x + 2y = -8 → 2y = -4x - 8 → y = -2x - 4