ALGEBRA FUNDAMENTALS
Basic Definitions
Algebra
Algebra is a branch of mathematics where we use letters (like x, y, a, b, c...) along with
numbers (1, 2, 3...) to represent unknown values and relationships.
Example: x + 5, y - 3, 2x, 3y, x + 5 = 10, 2x + 3 = 4, etc.
Expression
Expression is a combination of numbers, variables and mathematical operations (+, -,
×, ÷) without an equal sign (=).
Example: 3x + 5, 2x, 2a - 7, 4y² + 3y - 1....
Algebraic Equation
An algebraic equation is a mathematical statement that shows two expressions are
equal using an equals sign (=).
Example:
• x + 5 = 10
• 2a + 5 = 7
• y² + 2 = 16
Key Difference
Q: What is the difference between algebraic expressions and algebraic equations?
Answer: In algebraic expressions, we cannot solve the value of variable used, but in
algebraic equations, we can solve or find out the values of variables used because equal
sign (=) is given in equations.
Page 1 | Mathematics Study Series
, Terms and Coefficients
Understanding the components of algebraic equations.
(a) [5x + y + 10]
• No. of Terms = 3 terms
• coefficient of x = +5
• coefficient of y = +1
• Constant term = 10
(b) [x² - 3xy + 2y²]
• No. of Terms = 3
• coefficient of x² = +1
• coefficient of x = -3y
• coefficient of y² = 2
• coefficient of y = -3x
(c) [3x² + 4x¹ - 12]
• No. of Terms = 3
• coefficient of x² = +3
• coefficient of x = +4
• constant term = -12
(d) [2xy² + 3z]
• No. of Terms = 2
• coefficient of x = 2y²
• coefficient of y² = +2
• coefficient of z = +3
Page 2 | Mathematics Study Series
Basic Definitions
Algebra
Algebra is a branch of mathematics where we use letters (like x, y, a, b, c...) along with
numbers (1, 2, 3...) to represent unknown values and relationships.
Example: x + 5, y - 3, 2x, 3y, x + 5 = 10, 2x + 3 = 4, etc.
Expression
Expression is a combination of numbers, variables and mathematical operations (+, -,
×, ÷) without an equal sign (=).
Example: 3x + 5, 2x, 2a - 7, 4y² + 3y - 1....
Algebraic Equation
An algebraic equation is a mathematical statement that shows two expressions are
equal using an equals sign (=).
Example:
• x + 5 = 10
• 2a + 5 = 7
• y² + 2 = 16
Key Difference
Q: What is the difference between algebraic expressions and algebraic equations?
Answer: In algebraic expressions, we cannot solve the value of variable used, but in
algebraic equations, we can solve or find out the values of variables used because equal
sign (=) is given in equations.
Page 1 | Mathematics Study Series
, Terms and Coefficients
Understanding the components of algebraic equations.
(a) [5x + y + 10]
• No. of Terms = 3 terms
• coefficient of x = +5
• coefficient of y = +1
• Constant term = 10
(b) [x² - 3xy + 2y²]
• No. of Terms = 3
• coefficient of x² = +1
• coefficient of x = -3y
• coefficient of y² = 2
• coefficient of y = -3x
(c) [3x² + 4x¹ - 12]
• No. of Terms = 3
• coefficient of x² = +3
• coefficient of x = +4
• constant term = -12
(d) [2xy² + 3z]
• No. of Terms = 2
• coefficient of x = 2y²
• coefficient of y² = +2
• coefficient of z = +3
Page 2 | Mathematics Study Series
