(y²-7) ² - 4(y-7) -45

To simplify the expression (y²-7)² - 4(y-7) - 45, follow these steps:

Step 1: Expand the square term (y²-7)² using the formula (a-b)² = a² - 2ab + b².

(y²-7)² = (y²)² - 2(y²)(7) + (7)² = y⁴ - 14y² + 49

Step 2: Distribute -4 to both terms inside the parentheses.

-4(y-7) = -4y + 28

Step 3: Combine like terms.

Therefore, the simplified expression becomes:

(y²-7)² - 4(y-7) - 45 = y⁴ - 14y² + 49 - 4y + 28 - 45 = y⁴ - 14y² - 4y + 32