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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. + + =
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 ...
Get ready for all of today's NYT 'Connections’ hints and answers for #553 on Sunday, December 15, 2024. Today's NYT Connections puzzle for Sunday, December 15, 2024 The New York Times
New details about a study that warned against black plastic spatulas and other kitchen tools have come out. (Getty Creative) (Анатолий Тушенцов via Getty Images)
Like polynomials, rational expressions can also be generalized to n indeterminates X 1,..., X n, by taking the field of fractions of F[X 1,..., X n], which is denoted by F(X 1,..., X n). An extended version of the abstract idea of rational function is used in algebraic geometry.
During last night's game there was an on-court skit that missed the mark. The skit included bad decision making and poor communication. Simply put, we turned the ball over and we apologize.