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In mathematics, like terms are summands in a sum that differ only by a numerical factor. [1] Like terms can be regrouped by adding their coefficients. Typically, in a polynomial expression , like terms are those that contain the same variables to the same powers , possibly with different coefficients .
The number 3 is a constant term. [1] After like terms are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial + +, where is the variable, as having a constant term of .
This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms. Exponential function [ edit ]
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
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 ...
For example, if y is considered a parameter in the above expression, then the coefficient of x would be −3y, and the constant coefficient (with respect to x) would be 1.5 + y. When one writes a x 2 + b x + c , {\displaystyle ax^{2}+bx+c,} it is generally assumed that x is the only variable, and that a , b and c are parameters; thus the ...
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For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the variable y to be the unknown, and then the equation is solved by y = x – 1.