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The square of the sum of two terms
(a+b)^{2}=a^{2}+2ab+b^{2}

The square of the difference of two terms
(ab)^{2}=a^{2}2ab+b^{2}

The product of the sum and the difference of two terms.
(a+b)(ab)=a^{2}b^{2}

The product of two binomials having a common term.
(x+a)(x+b)=x^{2}+(a+b)x+ab

Legendre's Identity
(x+y)^{2}+(xy)^{2}=2(x^{2}+y^{2})

Two methods of synthetic division
 Horner's Method
 Ruffini's Method

Algebraic Term
formed by a numerical part and a literal part

coefficient
numerical part of an algebraic term

variables with corresponding indices
the literal part of an algebraic term

Algebraic expression
contains one or more algebraic terms

monomial
algebraic expression with one term

polynomial
algebraic expression with more than one term

binomial
has two algebraic terms

trinomial
algebraic expression with three terms

relative degree
degree with respect to a certain variable. it is equal to the index of that variable

absolute degree
it is the sum of the indices of all the variables in a term

Relative degree of a polynomial
it is the degree with respect to a certain variable. It is equal to the highest relative degree with respect to that variable of the terms in the polynomial.

absolute degree of a polynomial
it is the highest absolute degree of the terms in the polynomial.

complete polynomial
contains al the powers of that variable from zero to n