Factoring and Expanding (x²  5x + 4)(x²  9)
This expression involves two quadratic expressions multiplied together. We can simplify this expression by:

Factoring each quadratic:
 x²  5x + 4 factors into (x  4)(x  1)
 x²  9 is a difference of squares and factors into (x + 3)(x  3)

Multiplying the factored expressions:
 (x  4)(x  1)(x + 3)(x  3)

Expanding the product:
 We can expand this product by systematically multiplying each term in the first expression by each term in the second expression. This can be done using the distributive property or by using a technique like the FOIL method.
Here's the expansion in detail:
(x  4)(x  1)(x + 3)(x  3)

Expand (x  4)(x  1):
 (x²  5x + 4)(x + 3)(x  3)

Expand (x + 3)(x  3):
 (x²  5x + 4)(x²  9)

Expand (x²  5x + 4)(x²  9):
 x⁴  5x³ + 4x²  9x² + 45x  36

Combine like terms:
 x⁴  5x³  5x² + 45x  36
Therefore, the expanded and simplified form of (x²  5x + 4)(x²  9) is x⁴  5x³  5x² + 45x  36.