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Example:Subtracting Algebraic Expressions

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Like terms


In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. (Our solved example in mathguru.com uses this concept)

Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power. For example, 8xyz2 and −5xyz2 are like terms because they have the same variables and power while 3abc and 3ghi are unlike terms because they have different variables. Since the coefficient doesn't affect likeness, all constant terms are like terms.



If all terms in an expression are like terms, the expression can be simplified, or rewritten as a fraction or equation for mathematical purposes. For example, 2a, 2a are the same number and variable making it a like term.





Additive inverse

In mathematics, the additive inverse, or opposite, of a number a is the number that, when added to a, yields zero. The additive inverse of F is denoted −F.

For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive inverse of −0.3 is 0.3, because −0.3 + 0.3 = 0.

In other words, the additive inverse of a number is the number's negative. For example, the additive inverse of 8 is −8, the additive inverse of 10002 is −10002 and the additive inverse of x² is −(x²).





In mathematics, a polynomial (from Greek poly, "many" and medieval Latin binomium, "binomial") is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.


A polynomial is either zero, or can be written as the sum of one or more non-zero terms. The number of terms is finite. These terms consist of a constant (called the coefficient of the term) which may be multiplied by a finite number of variables (usually represented by letters). Each variable may have an exponent that is a non-negative integer, i.e., a natural number. The exponent on a variable in a term is called the degree of that variable in that term, the degree of the term is the sum of the degrees of the variables in that term, and the degree of a polynomial is the largest degree of any one term. Since x = x1, the degree of a variable without a written exponent is one. A term with no variables is called a constant term, or just a constant. The degree of a constant term is 0.

Two terms with the same variables raised to the same powers are called "like terms". Polynomials are added using the commutative, associative, and distributive laws, by combining like terms. For example, if


Description: P+Q=3x^2-2x+5xy-2+-3x^2+3x+4y^2+8 \,,

which can be simplified to


(Our solved example in mathguru.com uses this concept)

In general any expression can be considered to be a polynomial if it is built up from variables and constants using only addition, subtraction, multiplication, and raising expressions to constant positive whole number powers.

Since subtraction can be replaced by addition of the opposite quantity (Our solved example in mathguru.com uses this concept) and since positive whole number exponents can be replaced by repeated multiplication, all polynomials can be constructed from constants and variables using only addition and multiplication.





The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.