5(y+3x)-4(x-3y

To simplify the expression \( 5(y + 3x) - 4(x - 3y) \), follow these steps:

1. Distribute \( 5 \) in the first part: \[ 5(y + 3x) = 5y + 15x \]

2. Distribute \( -4 \) in the second part: \[ -4(x - 3y) = -4x + 12y \]

3. Now combine both results: \[ 5y + 15x - 4x + 12y \]

4. Combine like terms:

   • For \( x \) terms: \( 15x - 4x = 11x \)
   • For \( y \) terms: \( 5y + 12y = 17y \)

5. The simplified expression is: \[ 11x + 17y \]

Thus, the final result is: \[ 11x + 17y \]