Measurement of branching fractions and charge asymmetries in B± → ρ±π⁰ and B± → ρ⁰π± decays, and search for B⁰ → ρ⁰π⁰

We present measurements of branching fractions and charge asymmetries in B-meson decays to rho(+)pi(0), rho(0)pi(+), and rho(0)pi(0). The data sample comprises 89x10(6) Upsilon(4S)-->BBmacr; decays collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We find the charge-averaged branching fractions B(B+-->rho(+)pi(0))=[10.9+/-1.9(stat)+/-1.9(syst)]x10(-6) and B(B+-->rho(0)pi(+))=(9.5+/-1.1+/-0.9)x10(-6), and we set a 90% confidence-level upper limit B(B0-->rho(0)pi(0))