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As this example shows, when like terms exist in an expression, they may be combined by adding or subtracting (whatever the expression indicates) the coefficients, and maintaining the common factor of both terms. Such combination is called combining like terms, and it is an important tool used for solving equations.
A visual memory tool can replace the FOIL mnemonic for a pair of polynomials with any number of terms. Make a table with the terms of the first polynomial on the left edge and the terms of the second on the top edge, then fill in the table with products of multiplication. The table equivalent to the FOIL rule looks like this:
Terms that are either constants or have the same variables raised to the same powers are called like terms. If there are like terms in an expression, one can simplify the expression by combining the like terms. One adds the coefficients and keeps the same variable. + + =
A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that
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Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
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