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The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law. The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra. The term appears in William Betz's 1929 text Algebra for Today, where he states: [2]
In binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. Thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. The factor (2 −1) is a right arithmetic shift, a (0) results in no operation (since 2 0 = 1 is the multiplicative identity element), and a (2 1) results in a left arithmetic shift ...
As with the monomials, one would set up the sides of the rectangle to be the factors and then fill in the rectangle with the algebra tiles. [2] This method of using algebra tiles to multiply polynomials is known as the area model [3] and it can also be applied to multiplying monomials and binomials with each other.
The primitive part of such a polynomial is the quotient of the polynomial by its content. Thus a polynomial is the product of its primitive part and its content, and this factorization is unique up to the multiplication of the content by a unit of the ring of the coefficients (and the multiplication of the primitive part by the inverse of the ...
Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers , variables , and polynomials , along with their factorization and determining their roots .
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
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