Algebraic Expression: An algebraic expression is a mathematical phrase that includes numbers, variables (letters that represent unknown values), and arithmetic operations (addition, subtraction, multiplication, and division).

Example: ( 3x + 4 ), ( 5y – 2 ), and ( 2a + 3b – 5 ) are algebraic expressions where ( x ), ( y ), and ( a ), ( b ) are variables, and 3, 4, 5, and -2 are constants.

Terms: Terms are the parts of an algebraic expression that are separated by addition (+) or subtraction (-) signs.

Example: In the expression ( 3x + 4 ), there are two terms: ( 3x ) and ( 4 ).

Factors: Factors are the quantities that are multiplied together to form a term.

Example: In the term ( 3x ), 3 and ( x ) are factors.

Coefficients: The coefficient is the numerical part of a term that contains a variable.

Example: In the term ( 3x ), 3 is the coefficient.

Like Terms: Terms that have the same variable raised to the same power.

Example: ( 3x ) and ( 5x ) are like terms because they both contain ( x ) raised to the same power.

Unlike Terms: Terms that have different variables or the same variables raised to different powers.

Example: ( 3x ) and ( 4y ) are unlike terms because they contain different variables; similarly, ( 2x ) and ( 2x² ) are unlike terms because the variables are raised to different powers.

Addition: To add algebraic expressions, combine like terms by adding their coefficients.

Example: ( 3x + 4x = 7x ). Here, 3 and 4 are added because they are coefficients of like terms.

Subtraction: To subtract algebraic expressions, combine like terms by subtracting their coefficients.

Example: ( 5y – 2y = 3y ). Here, 2 is subtracted from 5 because they are coefficients of like terms.

Multiplication: To multiply algebraic expressions, multiply the coefficients and then multiply the variables.

Example: ( 3x × 4y = 12xy ). Here, 3 and 4 are multiplied to give 12, and ( x ) and ( y ) are multiplied to give ( xy ).

Division: To divide one algebraic expression by another, divide the coefficients and then divide the variables.

Example: ( 6x ÷ 3 = 2x ). Here, 6 is divided by 3 to give 2, and ( x ) remains as it is.

Translating Statements to Expressions: Convert verbal statements into algebraic expressions.

Example: The statement “Three more than twice a number ( x )” translates to the algebraic expression ( 2x + 3 ).

Combining Like Terms: Simplify expressions by combining like terms.

Example: The expression ( 3x + 2x – 5 ) can be simplified by combining like terms ( 3x ) and ( 2x ) to get ( 5x – 5 ).

Substitute and Simplify: Substitute the value of the variable into the expression and simplify.

Example: To evaluate the expression ( 3x + 4 ) for ( x = 2 ), substitute 2 for ( x ): ( 3(2) + 4 = 6 + 4 = 10 ).

Using Distributive Property: Expand expressions using the distributive property.

Example: Expand ( (a + b)(c + d) ): ( (a + b)(c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd ).

Common Algebraic Identities:

Example: ( (a + b)² = a² + 2ab + b² ).

Example: ( (a – b)² = a² – 2ab + b² ).

Example: ( (a + b)(a – b) = a² – b² ).

• Geometry: Algebraic expressions are used to calculate the area and perimeter of shapes.
• Example: The area of a rectangle with length ( l ) and width ( w ) is ( lw ).
• Physics: Algebraic expressions are used in formulas involving speed, distance, and time.
• Example: The formula for distance is Distance = Speed × Time.

• Example of Adding Like Terms: ( 3x + 4x = 7x ).
• Example of Forming Expressions: “Three more than twice a number ( x )” translates to ( 2x + 3 ).
• Example of Simplifying Expressions: ( 3x + 2x – 5 = 5x – 5 ).
• Example of Evaluating Expressions: If ( x = 2 ), then ( 3x + 4 ) becomes ( 10 ).
• Example of Expanding Binomials: ( (a + b)(c + d) = ac + ad + bc + bd ).

• Importance of Understanding Algebraic Expressions: Grasping the basics of algebraic expressions is crucial for solving algebraic equations and understanding more advanced mathematical concepts.
• Applications in Various Fields: Algebraic expressions are widely used in geometry, physics, engineering, and various other fields to model and solve problems.