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NCERT Class 8 Maths Chapter 13

Algebra Play

NCERT Class 8 Maths Chapter 13 (Ganita Prakash Part 2) makes algebra engaging through exploration of expressions, equations, and patterns. This CBSE chapter covers simplifying algebraic expressions, forming and solving linear equations, and understanding the power of algebra in generalising mathematical patterns. Students move from specific numbers to general rules — a key leap in mathematical thinking.

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Key Terms

Algebraic Expression
A combination of variables, numbers, and operations (like +, -, ×, ÷) without an equality sign; e.g., 3x + 5, 2y² - 4y + 1.
Equation
A mathematical statement asserting that two expressions are equal; has an equality sign; e.g., 2x + 3 = 11.
Variable
A symbol (usually a letter) that represents an unknown quantity or a quantity that can change; e.g., x, y, n.
Coefficient
The numerical factor of a term in an algebraic expression; in 7x², the coefficient is 7.
Linear Equation
An equation where the highest power of the variable is 1; e.g., 3x + 5 = 14. Its graph is a straight line.
Polynomial
An algebraic expression with one or more terms, each consisting of a variable raised to a non-negative integer power; e.g., x² + 3x - 2.
Substitution
Replacing a variable in an expression with a specific numerical value to evaluate the expression; e.g., if x=3, then 2x+1 = 2(3)+1 = 7.

Frequently Asked Questions

What is the difference between an expression and an equation Class 8 Maths?▾

An algebraic expression is a combination of variables and numbers without an '=' sign; e.g., 3x + 7, 5y². An equation has an '=' sign and asserts that two expressions are equal; e.g., 3x + 7 = 22. Expressions can be simplified; equations can be solved to find the value of the variable.

How do you solve a linear equation Class 8 NCERT?▾

To solve a linear equation: (1) Simplify both sides, (2) Collect all variable terms on one side, (3) Collect all constant terms on the other side, (4) Divide by the coefficient of the variable. Example: 3x + 7 = 22; 3x = 15; x = 5. Always check: substitute back — 3(5)+7 = 22 ✓.

What are like and unlike terms in algebra Class 8?▾

Like terms have the same variable raised to the same power: 3x and 7x are like terms (both have x¹); 4x² and -2x² are like terms. Unlike terms have different variables or different powers: 3x and 5y are unlike (different variables); 3x and 3x² are unlike (different powers). Only like terms can be added or subtracted.

What are algebraic identities Class 8 Maths?▾

Key algebraic identities in Class 8: (a+b)² = a²+2ab+b², (a-b)² = a²-2ab+b², (a+b)(a-b) = a²-b². These are universally true for all values of a and b. They can be used as shortcuts: e.g., 99² = (100-1)² = 10000-200+1 = 9801. NCERT Class 8 Chapter 13 explores how and why these identities work.

How is algebra used to generalise patterns Class 8?▾

Algebra lets us express patterns as general rules. For example, the pattern 1, 3, 5, 7, ... (odd numbers) can be written as 2n-1 for n=1,2,3,... This formula works for any term. Similarly, the perimeter of a square with side s is always 4s, no matter what s is. Algebra converts specific observations into universal rules — the power of mathematics.

What is factorisation in Class 8 Algebra?▾

Factorisation is expressing an algebraic expression as a product of its factors. Methods include: (1) Taking out common factors: 6x + 9y = 3(2x + 3y), (2) Using identities: x² - 9 = (x+3)(x-3), (3) Regrouping: ax + ay + bx + by = a(x+y) + b(x+y) = (a+b)(x+y). Factorisation is the reverse of expansion and is very important for solving higher algebra problems.

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