5 y − 1 ) ⋅ ( 4 y + 9 ) = (5y−1)⋅(4y+9)=

To simplify the expression \((5y - 1)(4y + 9)\), you can use the distributive property (also known as the FOIL method for binomials). Here's the step-by-step calculation:

\[ (5y - 1)(4y + 9) \]

1. First: Multiply the first terms: \[ 5y \cdot 4y = 20y^2 \]

2. Outer: Multiply the outer terms: \[ 5y \cdot 9 = 45y \]

3. Inner: Multiply the inner terms: \[ -1 \cdot 4y = -4y \]

4. Last: Multiply the last terms: \[ -1 \cdot 9 = -9 \]

Now, combine all these results together: \[ 20y^2 + 45y - 4y - 9 \]

Combine like terms: \[ 20y^2 + (45y - 4y) - 9 = 20y^2 + 41y - 9 \]

So, the expression \((5y - 1)(4y + 9)\) simplifies to: \[ \boxed{20y^2 + 41y - 9} \]