Algebraic Expressions Class 7 Maths Chapter Notes

What are Algebraic Expressions?

In mathematics, we often use letters like x, y, a, or b to represent unknown numbers. These letters are called variables. An algebraic expression is a combination of constants (numbers with a fixed value, like 4, -10, or 1/2) and variables, connected by mathematical operations such as addition (+), subtraction (-), multiplication (×), and division (÷). For example, 4x + 7 is an algebraic expression. Here, x is the variable, 4 is its coefficient, and 7 is the constant. The expression is made up of parts called terms, which are added or subtracted. In 4x + 7, the terms are 4x and 7. Expressions are the fundamental building blocks of algebra and are used to represent real-world situations in a mathematical form. Unlike an equation, an expression does not have an equals sign (=) with a value on the other side.

Key Terms in Algebraic Expressions

Variable

A symbol, usually a letter (like x, y, a), that represents an unknown quantity and can take various numerical values.

Constant

A symbol or number that has a fixed numerical value. Example: 5, -9, π.

Term

A single part of an expression, which can be a constant, a variable, or a product of constants and variables. Terms are separated by + or - signs. Example: In 2a - 3b + 5, the terms are 2a, -3b, and 5.

Coefficient

The numerical factor in a term. Example: In the term 7xy, the coefficient is 7.

Like Terms

Terms that have the same algebraic factors (same variables raised to the same power). Example: 3xy and -5xy are like terms.

Unlike Terms

Terms that have different algebraic factors. Example: 3xy and 3x are unlike terms.

Monomial

An algebraic expression containing only one term. Example: 5x².

Binomial

An algebraic expression containing two unlike terms. Example: a + 2b.

Trinomial

An algebraic expression containing three unlike terms. Example: x + y - 3.

Polynomial

A general term for an algebraic expression with one or more terms, where the variables have non-negative integer exponents.

Components of an Expression

Like Terms vs. Unlike Terms

How to Add and Subtract Algebraic Expressions

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Worked Examples

• {"label":"Addition","content":"Add 7x - 4y + 5z and 2x + 3y.\nSolution:\nGroup like terms: (7x + 2x) + (-4y + 3y) + 5z\nCombine coefficients: (7+2)x + (-4+3)y + 5z\nResult: 9x - y + 5z"}
• {"label":"Subtraction","content":"Subtract 4a - 2b + c from 9a - b - 3c.\nSolution:\nWrite as (9a - b - 3c) - (4a - 2b + c)\nChange signs of the second expression: 9a - b - 3c - 4a + 2b - c\nGroup like terms: (9a - 4a) + (-b + 2b) + (-3c - c)\nResult: 5a + b - 4c"}
• {"label":"Finding the Value","content":"Find the value of 3m² - 2m - 7 when m = -2.\nSolution:\nSubstitute m = -2 into the expression: 3(-2)² - 2(-2) - 7\nCalculate powers first: 3(4) - 2(-2) - 7\nMultiply: 12 - (-4) - 7 which is 12 + 4 - 7\nResult: 16 - 7 = 9"}

Must Remember

• Only like terms can be added or subtracted.
• The sign of a term belongs to the term. For example, in x - 5y, the second term is -5y.
• When subtracting an expression, change the sign of every term within the brackets and then add.
• The coefficient of a term like x is 1, and for -x it is -1.
• An expression does not have an equals sign. An equation does.
• Monomials have 1 term, Binomials have 2 unlike terms, Trinomials have 3 unlike terms.
• The value of an expression changes as the value of its variable(s) changes.
• Always follow the order of operations (BODMAS/PEMDAS) when substituting values into an expression.

Exam Tip: Avoid Subtraction Errors

A very common mistake is forgetting to change the signs of all terms when subtracting an expression. For example, when calculating (5x + 3) - (2x - 1), many students incorrectly write 5x + 3 - 2x - 1. The correct method is to distribute the negative sign to both terms inside the bracket: 5x + 3 - 2x + 1. Always use brackets and carefully change the sign of every term being subtracted to avoid losing marks.

Quick Revision Check

• Q: Identify the terms and their coefficients in the expression 5xyz² - 3zy. A: The terms are 5xyz² and -3zy. The coefficient of the first term is 5, and the coefficient of the second term is -3.
• Q: Classify the following as monomial, binomial, or trinomial: (a) 4y - 7z (b) 100 (c) a + b + c A: (a) Binomial (two unlike terms), (b) Monomial (one term), (c) Trinomial (three unlike terms).
• Q: Add: p² - q² and 2p² + 3q² A: (p² + 2p²) + (-q² + 3q²) = 3p² + 2q²
• Q: If x = 2, what is the value of the expression x² + 2x - 1? A: Substitute x = 2: (2)² + 2(2) - 1 = 4 + 4 - 1 = 7.

Frequently Asked Questions

Frequently Asked Questions