Chapter 5 - Algebraic Expressions Revision Notes - Class 7 Mathematics

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📌 Key Points

A variable is a letter (x, y, a, b) representing an unknown number.
A constant is a fixed number (2, 5, -3) that doesn't change.
Coefficient is the number multiplying a variable. In 5x, coefficient is 5.
Like terms have the same variable(s) with same powers: 3x and 5x, or 2x² and -4x².
Unlike terms have different variables or powers: 3x and 3y, or 2x and 2x².
Monomial has 1 term (5x), Binomial has 2 terms (x + 3), Trinomial has 3 terms (x² + 2x + 1).
Combine only like terms by adding/subtracting their coefficients.
Distributive property: a(b + c) = ab + ac. Use for multiplication and division.
To subtract expressions, distribute negative sign to all terms in second expression.
When dividing expressions, divide each term separately by the divisor.
Degree of a term is the sum of exponents of all variables in that term.
Polynomial is an expression with one or more terms.
To simplify, combine like terms and reduce to the lowest terms.
Algebraic expressions can represent real-life quantities: distance = speed × time = 60t.
Always check answers: substitute values back to verify simplification is correct.

📘 Important Definitions

Variable

A letter (x, y, a) representing an unknown or changing number.

Constant

A fixed number that doesn't involve variables.

Coefficient

The number multiplying a variable. In 5x, the coefficient is 5.

Like Terms

Terms with the same variable(s) raised to the same power (e.g., 3x and 5x).

Unlike Terms

Terms with different variables or different powers (e.g., 3x and 3y).

Monomial

An algebraic expression with exactly one term (e.g., 5x, 3a²).

Binomial

An algebraic expression with exactly two terms (e.g., x + 3, 2x - 5).

Polynomial

An expression with one or more terms combined by addition or subtraction.

🔢 Formulas & Laws

Distributive Property

a(b + c) = ab + ac

Use for multiplication and division

Combining Like Terms

ax + bx = (a + b)x

Add or subtract coefficients of like terms

Subtraction of Expressions

(a + b) - (c + d) = a + b - c - d

Distribute negative sign to all terms in second expression

Division of Expression

(ax + b) ÷ c = (a/c)x + (b/c)

Divide each term separately

Degree of Term

Sum of exponents of all variables

Example: Degree of 5x³y² is 3 + 2 = 5

⚠️ Common Mistakes

✗ Wrong: Confusing coefficient with variable: In 5x, 5 is coefficient, not the variable

✓ Correct: Coefficient is the number; variable is the letter

✗ Wrong: Combining unlike terms: 3a + 2b = 5ab (WRONG)

✓ Correct: Unlike terms cannot be combined. Keep as 3a + 2b

✗ Wrong: Forgetting to distribute in subtraction: (5x + 3) - (2x + 1) = 5x + 3 - 2x + 1 (WRONG)

✓ Correct: (5x + 3) - (2x + 1) = 5x + 3 - 2x - 1 = 3x + 2

✗ Wrong: Incomplete distribution: 2(x + 3) = 2x + 3 (WRONG)

✓ Correct: 2(x + 3) = 2x + 6 (distribute 2 to all terms)

✗ Wrong: Misreading word problems: 'x increased by 5' means x + 5, NOT 5x

✓ Correct: 'x increased by 5' = x + 5; 'five times x' = 5x

📝 Exam Focus

These questions are frequently asked in CBSE exams:

Identifying and combining like terms

1m★★★

Simplifying algebraic expressions

2m★★★

Expanding brackets using distributive property

2m★★

Addition and subtraction of polynomials

2m★★

Word problems converted to algebraic expressions

3m★★

Evaluating expressions for given variable values

1m★★

🎯 Last-Minute Recall