Algebraic Identities Exercise 4.4 Class 9 Maths NCERT Solutions

The Algebraic Identities Exercise 4.4 solutions cover all three questions of the fourth exercise set from the new Ganita Manjari book. This is the full NCERT Solutions Class 9 Maths Chapter 4 Algebraic Identities Exercise 4.4, where you turn quadratics into products by splitting the middle term and use the difference of squares to multiply cleverly.

• Questions solved: 3 open-ended questions, with all sub-parts worked out.
• Main skill: factoring Ax² + Bx + C and using a² - b² = (a+b)(a-b).
• Chapter link: splitting the middle term is the workhorse for the rest of algebra.

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 4.4 Cover?

This set is about factoring quadratics and picking quick product shortcuts. To factor Ax² + Bx + C, you find two numbers whose product is A × C and whose sum is B, then split and group. You also match products to a shape: (a ± b)² for squares, a² - b² for symmetric pairs, and (x+p)(x+q) for numbers near a common base. The set mixes fill-in-the-blank factors, mental products, and full factoring, including three-square trinomials. Choosing the right shape at a glance is the habit that makes each part quick and keeps your arithmetic clean.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Algebraic Identities Exercise 4.4 Question Breakdown

The table below shows what each of the three questions asks, so you know the exact skill before you start.

Sample Solved Question from Exercise 4.4

Here is Question 2, part (iii), solved step by step so you can see the method used across the set.

Question: Find 23 × 17 using a suitable identity.

Step 1. Notice the two numbers straddle a round figure. Both are 20 ± 3.

Step 2. Use the difference of squares, a² - b² = (a+b)(a-b), with a = 20 and b = 3.

Step 3. Substitute. 23 × 17 = (20+3)(20-3) = 20² - 3² = 400 - 9.

Final answer. 23 × 17 = 391.

How to Use These Algebraic Identities Exercise 4.4 Solutions

Try each part on your own first, then open the Collegedunia solution to check every line. The steps split the middle term with the A × C rule and fix signs from the constant before any trial. For the product questions, they show you which identity to pick at a glance, so mental arithmetic stays fast and clean.

• Use A × C: two numbers with product A × C and sum B split the middle term.
• Match the shape: square, difference of squares, or (x+p)(x+q) for a shared base.
• Self-check: multiply your two factors back to rebuild the original expression.

More Class 9 Maths Algebraic Identities Solutions

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