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What is the difference multiplying binomials with factoring polynomials into binomial factors?
It's the difference between multiplication and division. Multiplying binomials is combining them. Factoring polynomials is breaking them apart.
What is the last step when multiplying binomials?
Combining like terms.
When multiplying binomials that turn out negative do you add or subtract exponents?
When multiplying numbers with exponents, you add the exponents.
Is a method that uses a pattern to simplify multiplying two binomials together?
Foil
FOIL is a method that uses a pattern to simplify two binomials together?
multiplying
FOIL is a method that uses a pattern to simplify multiplying two together?
binomials
Why is the FOIL method not needed when multiplying two 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.
What is a product of a Binomials?
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.
What is 11ww-22 when multiplying monomials and binomials?
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).
What is an acronym used to remember the steps needed to multiply two 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.
How is factoring a polynomial different from multiplying two binomials?
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.
Is the product of two binomials always be a trinomial?
No, the product of two binomials is not always a trinomial; it is typically a trinomial when both binomials are of the form (ax + b)(cx + d) where at least one of the coefficients is non-zero. However, if either binomial includes a term that results in a cancellation or if both binomials are constants, the result could be a polynomial of a lower degree or a constant. For example, multiplying (x + 2)(x - 2) results in a difference of squares, yielding a binomial (x² - 4), not a trinomial.
