Depends on the kind of binomials.
Case 1:
If both binomials have different terms, then use the distribution property. Each term of one binomial will multiply both terms of the other binomial. After distribution, combine like terms, and it's done.
Case 2:
If both binomials have exactly the same terms, then work as in the 1st case, or use the formula for suaring a binomial, (a ± b)2 = a2 ± 2ab + b2.
Case 3:
If both binomials have terms that only differ in sign, then work as in the 1st case, or use the formula for the sum and the difference of the two terms, (a - b)(a + b) = a2 - b2.
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It is only not needed if you know of another method. If FOIL is the only way you know to multiply two binomials, then it is definitely needed.
When multiplying numbers with exponents, you add the exponents.
To find the factor of 2 binomials
You don't need any acronym; just multiply every monomial on the left with every monomial on the right. The same goes for multiplying a binomial with a trinomial, two trinomials, or in fact for multiplying any polynomial by any other polynomial.
The foil method in algebra is used to "multiply linear binomials."The FOIL method is used in elementary algebra as a guide for solving algebraic problems.