NCERT Solutions Class 9 Maths Chapter 4 — Exploring Algebraic Identities#

Chapter 4 develops the standard algebraic identities such as $(a+b)^2 = a^2 + 2ab + b^2$ and $(a+b)(a-b) = a^2 - b^2$. You will use these identities to expand expressions quickly, factorise polynomials, and simplify complex algebraic calculations.

Exercises#

• Exercise Set 4.1 — Expanding with $(a + b)^2$, quick squares of numbers (2 questions)
• Exercise Set 4.2 — Factoring perfect squares, squares using $(a - b)^2$ (2 questions)
• Exercise Set 4.3 — Squares of numbers, factoring with $(a + b + c)^2$, testing whether an equation is an identity (4 questions)
• Exercise Set 4.4 — Splitting the middle term, quick products, three-term squares (3 questions)
• Exercise Set 4.5 — Simplifying rational expressions (1 question)
• End-of-Chapter Exercises — Cube identities, cubes of numbers, factorisation, rational expressions and word problems (13 questions)

What you will learn#

• The identities for $(a + b)^2$, $(a - b)^2$, $(a + b)(a - b)$ and $(a + b + c)^2$, with picture proofs.
• Cube identities and products of the form $(x + a)(x + b)$.
• Quick mental squares and products of numbers using identities.
• Factorisation by splitting the middle term, and simplifying rational expressions.

Key formulas and results#

• $(a + b)^2 = a^2 + 2ab + b^2$
• $(a - b)^2 = a^2 - 2ab + b^2$
• $(a + b)(a - b) = a^2 - b^2$
• $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

Read and revise#

• NCERT Class 9 Maths Chapter 4 (PDF) — the Ganita Manjari Part I chapter itself.
• All Class 9 Maths chapters from Ganita Manjari Part I and Part II.

Frequently asked questions#