NCERT Ganita Manjari, Class 9, textbook pages 68–91 (Part I)

How to help your child with Class 9 Maths Chapter 4, Exploring Algebraic Identities, at home

Identities and factorisation, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

a²b²(a + b)²= a²+2ab+b²

NCERT Class 9 Maths Chapter 4 Exploring Algebraic Identities: what it teaches

Your teen proves and uses identities such as (a + b)², (a − b)², (a + b)(a − b), (a + b + c)² and cube identities, often with area and volume models, and uses them to factorise and calculate quickly.

Why it matters later. Identities are used throughout Classes 10–12 in polynomials, quadratic equations and calculus.

See it: this chapter in pictures

x² − 49= x² − 7²= (x + 7)(x − 7)
Spot the squares.
105 × 95= 100² − 5²= 9975
Identities speed up calculation.
(a + b)³= a³ + 3a²b + 3ab² + b³check: a = b = 1 → 8
Check expansions with small numbers.

You need

  • graph paper
  • cardboard squares and rectangles
  • a calculator

Tonight’s 30 minutes

  1. Build (a + b)² with cardboard pieces and write the identity.
  2. Factorise x² − 49 as (x + 7)(x − 7).
  3. Calculate 105 × 95 mentally with an identity.
  4. Expand (x + 2)³ and check with x = 1.

Words to use

  • identity
  • expand
  • factorise
  • square
  • cube
  • area model

Watch for

  • Forgetting the middle term 2ab. Draw the square to see both ab rectangles.
  • Sign errors in (a − b)³. Check any expansion by substituting small numbers.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You51 × 49 quickly?

Your child50² − 1 = 2499.

A game for this week: Identity sprint

  1. Write products like 99², 51 × 49.
  2. Solve mentally with identities.
  3. Check with a calculator.
  4. Fastest correct wins.

A 5-day plan, 30 minutes a day

  1. Day 1Area model of (a + b)².
  2. Day 2Difference of squares.
  3. Day 3Mental maths.
  4. Day 4Cube identities.
  5. Day 5Identity sprint.

Everyday moments to practise

  • Mental calculation.
  • Area of extended plots.
  • Design and architecture.
  • Physics formulas.

Quick check

Ask these at the end of the week. Tap to see the answer.

Factorise x² − 49.

(x + 7)(x − 7).

105 × 95?

9975.

(x + 2)³ at x = 1?

27.

Ready for the next chapter when your child…

  • Recalls and proves key identities.
  • Factorises using identities.
  • Applies them to calculation.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

Which identities are in Class 9?

Squares, difference of squares, (a + b + c)², cubes and a³ + b³ + c³ − 3abc.

How to check an expansion?

Substitute a small number on both sides.

Why learn identities?

They speed up factorising and calculation.