(y²-7) ² - 4(y-7) -45

To simplify the expression, let's expand the squares and simplify the subtraction and multiplication operations.

Starting with the first term: (y² - 7)² = (y² - 7)(y² - 7) = y⁴ - 7y² - 7y² + 49 = y⁴ - 14y² + 49

Now, simplifying the second term: -4(y - 7) = -4y + 28

Now, let's simplify the expression by substituting the expanded terms back in: (y² - 7)² - 4(y - 7) - 45 = y⁴ - 14y² + 49 - 4y + 28 - 45

Combining like terms: = y⁴ - 14y² - 4y + 32 - 45

= y⁴ - 14y² - 4y - 13