Use F.O.I.L. to multiply complex binomials. The acronym represents the idea of multiplying the first terms, then the outer terms, the inner terms and finally the last terms. For instance, say you had the following complex binomials: (2 + 5y)(3 - y). You would multiply the first terms, 2 times 3, and end up with 6.
Multiply the outer terms. For this example, that would be 2 multiplied by -y, resulting in -2y.
Multiply the inner terms. For this example, that would be 5y multiplied by 3, resulting in 15y.
Multiple the last terms of the binomials. This would be 5y multiplied by y, resulting in 5y^2.
Write out the new terms and combine any like terms. The complex binomials would be expressed as 6 - 2y + 15y - 5y^2. Since 15y - 2y can be simplified, the final expression is simplified to 6 + 13y - 5y^2.