Algebraic Expressions Formulas - Mathematics Class 7

Learn important formulas from the Algebraic Expressions chapter of Class 7 Mathematics with examples, variables and applications.

📐 Algebraic Expressions Formulas

Complete collection of formulas with explanations and examples

Product of Powers

$$a^m x a^n = a^(m+n)$$

Description: Product of Powers is a standard relation used in algebraic-expressions.

Example:

Apply the relation: a^m x a^n = a^(m+n)

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Simple Equation

$$ax + b = c$$

Description: Simple Equation is a standard relation used in algebraic-expressions.

Variables:

  • x = unknown

Example:

Apply the relation: ax + b = c

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Quick Reference

Product of Powers: $a^m x a^n = a^(m+n)$
Simple Equation: $ax + b = c$

💡 Worked Examples

Step-by-step solutions using Algebraic Expressions formulas

Example 1: Solving Quadratic Equation

Quadratic Formula
Problem:

Solve: 2x² + 5x + 3 = 0

Solution:
  1. Identify coefficients: a = 2, b = 5, c = 3
  2. Apply quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
  3. Calculate discriminant: Δ = 5² - 4(2)(3) = 25 - 24 = 1
  4. Substitute values: x = (-5 ± √1) / 4 = (-5 ± 1) / 4
  5. Find roots: x₁ = (-5 + 1)/4 = -1, x₂ = (-5 - 1)/4 = -3/2
Answer:

x = -1 or x = -3/2

Example 2: Arithmetic Progression Sum

AP Sum Formula
Problem:

Find the sum of first 10 terms of AP: 2, 5, 8, 11, ...

Solution:
  1. Identify: a = 2 (first term), d = 3 (common difference), n = 10
  2. Apply formula: Sₙ = n/2[2a + (n-1)d]
  3. Substitute: S₁₀ = 10/2[2(2) + (10-1)(3)]
  4. Simplify: S₁₀ = 5[4 + 9(3)] = 5[4 + 27] = 5(31)
  5. Calculate: S₁₀ = 155
Answer:

Sum = 155

🎯 Practice Problems

Try these problems to test your understanding:

Practice Problem 1

Solve the quadratic equation: x² - 7x + 12 = 0

Practice Problem 2

Find the area of a circle with diameter 14 cm.

Practice Problems

Check Your Formula Recall

Write each formula once, define every variable, then solve one direct substitution problem before moving to mixed questions.

Apply Algebraic Expressions

Pick two formulas from this page and create your own values for the variables. Verify units and signs before calculating.

Derivation Notes

Focus on how the formula is built, not only the final expression. Derivations help with board-exam reasoning and multi-step application questions.

  • Start from the definition or identity used in the chapter.
  • Write assumptions clearly before substituting values.
  • Track units through each step to catch calculation mistakes.

Where These Formulas Are Used

Board Exam Problems

Use these formulas for direct numerical questions, proof-based steps, and short-answer reasoning in Mathematics.

Competitive Practice

Memorize the condition of use for each formula so you can identify the right expression quickly under timed practice.

Related Formula Chapters

Algebraic Expressions 2 formulas Geometry 3 formulas Mensuration And Data 4 formulas Percentage And Proportion 2 formulas Rational Numbers 3 formulas

These Algebraic Expressions formulas help students revise concepts quickly and apply equations accurately in exam-style problems.

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