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Algebraic Expressions and Operations

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Algebraic expressions are the language of algebra, modeling unknown quantities through variables, constants, and coefficients. This overview covers the components of expressions, such as terms and variables, and explains how to translate word problems into algebraic terms. It delves into the differences between numerical and algebraic expressions, and outlines the processes of evaluating, simplifying, and factorising expressions to uncover underlying mathematical relationships.

Understanding Mathematical Expressions

Mathematical expressions are a crucial part of algebra that model situations involving unknown quantities. These expressions are made up of terms, which may include variables, constants, and coefficients, linked by arithmetic operations such as addition, subtraction, multiplication, or division. A well-formed expression follows the rules of arithmetic, ensuring that operators are used correctly and parentheses are properly matched. For example, the expression \(2x+1\) is valid, combining a variable \(x\), a coefficient \(2\), and a constant \(1\) with an addition operation. In contrast, \(2x+\times 1\) is invalid due to the misuse of operators.
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Components and Examples of Expressions

Mathematical expressions consist of variables, which stand for unknown values; terms, which are the separated parts of an expression that include numbers, variables, or both; coefficients, which are the numerical multipliers of variables; and constants, which are fixed numbers. In the expression \(6a+3\), for instance, \(6\) is the coefficient, \(a\) is the variable, and \(3\) is the constant. Other examples of expressions are \((x+1)(x+3)\), representing the product of two binomials, \(6x-15y+12\), a linear combination of terms with variables \(x\) and \(y\), and \(\frac{x}{4}+\frac{x}{5}\), which illustrates the addition of rational expressions.

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00

Define variables in expressions

Variables represent unknown values, e.g., 'a' in '6a+3'.

01

Explain coefficients

Coefficients are numerical multipliers of variables, e.g., '6' in '6a'.

02

Identify constants

Constants are fixed numbers in expressions, e.g., '3' in '6a+3'.

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