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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.
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 ...
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. + + =
The third power of the trinomial a + b + c is given by (+ +) = + + + + + + + + +. This can be computed by hand using the distributive property of multiplication over addition and combining like terms, but it can also be done (perhaps more easily) with the multinomial theorem.
Layers of Pascal's pyramid derived from coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial – the number of terms is clearly a triangular number. In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by
When the exponent is zero, the result is always 1 (e.g. is always rewritten to 1). [17] However , being undefined, should not appear in an expression, and care should be taken in simplifying expressions in which variables may appear in exponents.
The polynomial () (+) is a cubic polynomial: after multiplying out and collecting terms of the same degree, it becomes + +, with highest exponent 3.. The polynomial (+ +) + (+ + +) is a quintic polynomial: upon combining like terms, the two terms of degree 8 cancel, leaving + + + +, with highest exponent 5.
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.