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.
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Mathematical expressions are made up of terms, which include variables, constants, and coefficients, linked by arithmetic operations
A well-formed expression follows the rules of arithmetic, ensuring that operators are used correctly and parentheses are properly matched
Examples of expressions include linear combinations, products of binomials, and addition of rational expressions
Translating word problems into mathematical expressions is a key skill in algebra that involves interpreting language and representing it with variables and operations
Examples of translations include expressions for "five more than a number," "three-fourths of a number," and "the product of a number with twelve."
Numerical expressions contain only numbers and operations, while algebraic expressions include variables that represent unknown quantities
Examples of numerical expressions include simple arithmetic operations, while examples of algebraic expressions include rational expressions and polynomials
Evaluating expressions involves performing operations to find their value, often for specific variable values
Simplifying expressions means reducing them to a more basic or compact form without changing their value, often by combining like terms and applying the distributive property
Factorising expressions involves rewriting them as a product of simpler expressions, often by identifying a greatest common factor or recognizing patterns
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'.
