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In mathematics, an algebraic expression is an expression built up from constants (usually, rational or algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
A technique for multiplying two binomials in an algebraic expression using distributive law. First stated by. William Betz. First stated in. 1929; 95 years ago. ( 1929) In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials [ 1] —hence the method may be referred to as the FOIL method.
Algebraic equation. In mathematics, an algebraic equation or polynomial equation is an equation of the form , where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, is an algebraic equation with integer coefficients and. is a multivariate polynomial equation over the rationals.
One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...
In algebra, a number that is the multiplier of a variable or expression (e.g., the 3 in ) is called a coefficient. The result of a multiplication is called a product . When one factor is an integer, the product is a multiple of the other or of the product of the others.
Algebraic function. In mathematics, an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions using a finite number of terms, involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional ...
An algebraic expression is an expression built up from algebraic constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by a rational number). [10] For example, 3x 2 − 2xy + c is an algebraic expression. Since taking the square root is the same as raising to the power 1 / 2 ...
Cross-multiplication. In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling ...
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