to simplify the equation
It's the difference between multiplication and division. Multiplying binomials is combining them. Factoring polynomials is breaking them apart.
Combining like terms.
When multiplying numbers with exponents, you add the exponents.
Foil
multiplying
binomials
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.
A product of binomials refers to the result of multiplying two binomial expressions, which are algebraic expressions containing two terms. For example, multiplying ((a + b)) and ((c + d)) results in a new expression obtained through the distributive property, leading to (ac + ad + bc + bd). This process is often visualized using the FOIL method (First, Outer, Inner, Last) for binomials. The resulting expression is a polynomial that may have more than two terms.
To simplify the expression (11ww - 22) when multiplying monomials and binomials, you first recognize that it consists of a monomial (11ww) and a constant term (-22). If you were to multiply it by a binomial, such as ((x + y)), you would distribute each term in the binomial to both terms in the expression. For example, multiplying by ((x + y)) would yield (11ww \cdot x + 11ww \cdot y - 22 \cdot x - 22 \cdot y).
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 same way that factoring a number is different from multiplying two factors. In general, it is much easier to multiply two factors together, than to find factors that give a certain product.
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.