Algebraic Identities Exercise 4.5 Class 9 Maths NCERT Solutions

The Algebraic Identities Exercise 4.5 solutions cover the full question of the fifth exercise set from the new Ganita Manjari book. This is the complete NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities Exercise 4.5, where you use factoring to simplify rational expressions and cancel the common factors cleanly.

• Questions solved: 1 question with six rational expressions, each simplified in full.
• Main skill: factor the top and bottom, then cancel only whole common factors.
• Chapter link: this ties together the square, cube, and difference identities.

These solutions are prepared by subject teachers, matched to the current 2026-27 NCERT, and checked step by step so a Class 9 student can follow each line.

What Does Algebraic Identities Exercise 4.5 Cover?

This set uses factoring to simplify rational expressions, which are fractions with algebra on the top and bottom. The method is always the same: factor the numerator and the denominator completely, then cancel every whole factor they share. The six parts pull in the tools of the chapter, including (a ± b)², (a-b)³, the difference of squares a² - b², and the three-variable form a³ + b³ + c³ - 3abc. One part does not reduce at all, which teaches you that not every fraction simplifies.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Algebraic Identities Exercise 4.5 Question Breakdown

The single question has six rational expressions to simplify. The list below shows the identity behind each part.

• Part (i): two quadratics to split; the fraction shares no factor, so it stays as it is.
• Part (ii): a cube (n-m)³ over a square, reducing to n-m5.
• Part (iii): the three-variable form a³ + b³ + c³ - 3abc over a trinomial square.
• Part (iv): a perfect square over a difference of squares.
• Part (v): four quadratics that cancel fully to give 1.
• Part (vi): a degree-four top, factored twice by the difference of squares.

Sample Solved Question from Exercise 4.5

Here is part (iv), solved step by step so you can see the method used across the set.

Question: Simplify 4y² - 20yz + 25z²25z² - 4y².

Step 1. Factor the top. It is a perfect square, 4y² - 20yz + 25z² = (5z - 2y)².

Step 2. Factor the bottom. It is a difference of squares, 25z² - 4y² = (5z - 2y)(5z + 2y).

Step 3. Cancel the common factor (5z - 2y) from top and bottom.

Final answer. (5z - 2y)²(5z - 2y)(5z + 2y) = 5z - 2y5z + 2y.

How to Use These Algebraic Identities Exercise 4.5 Solutions

Try each part on your own first, then open the Collegedunia solution to check every line. The steps name the identity for each fraction, factor the top and bottom in full, and only then cancel. A short number check at the end confirms each result, which is a habit worth copying into your own work.

• Factor fully: split the top and the bottom into brackets before you cancel anything.
• Cancel factors, not terms: only whole bracketed factors can be removed.
• Number check: plug in simple values to confirm your simplified fraction.

More Class 9 Maths Algebraic Identities Solutions

Use the table below to open the full chapter page or any other exercise of this chapter.