Factor Completely: \( 15 a u-6 a v-25 y u+10 y v \)

To factor the expression \( 15au - 6av - 25yu + 10yv \), we’ll first group the terms: \[ (15au - 6av) + (-25yu + 10yv) \] Now, factor out the common factors from each group: From the first group \( 15au - 6av \), we can factor out \( 3a \): \[ 3a(5u - 2v) \] From the second group \( -25yu + 10yv \), we can factor out \(-5y\): \[ -5y(5u - 2v) \] Now, our expression looks like this: \[ 3a(5u - 2v) - 5y(5u - 2v) \] Notice that \( (5u - 2v) \) is a common factor: \[ (5u - 2v)(3a - 5y) \] Thus, the completely factored form of the original expression is: \[ (5u - 2v)(3a - 5y) \]