Simplification of Algebraic Expressions

Class 7 Maths · Chapter 4: Expressions using Letter-Numbers · NCERT Ganita Prakash section 4.4

Learn

The perimeter of a rectangle is length + breadth + length + breadth = l + b + l + b. Terms can be added in any order, so this is l + l + b + b = 2l + 2b. Both forms always give the same value: for l = 3, b = 4, both are 14. We call 2l + 2b the simplified form.

l + b + l + b = 2l + 2b

Like terms have the same letter-number: 5c, 3c and 10c are like terms, and 5c + 3c + 10c = (5 + 3 + 10)c = 18c. Terms with different letters, like 18c and 11d, are unlike and cannot be joined: 18c + 11d is already simplest. A shape split into two rectangles shows it: 4v + 3v = 7v.

5c + 3c + 10c = 18c · 4v + 3v = 7v

Subtracting expressions: renting x chairs at ₹40 and y tables at ₹75, you get ₹6 and ₹10 back each on return. You pay (40x + 75y) − (6x + 10y) = 40x + 75y − 6x − 10y = 34x + 65y. Open the brackets (signs change after a minus), then add like terms.

(40x + 75y) − (6x + 10y) = 34x + 65y

Equal or not? 5u means 5 times u; 5 + u means 5 more than u. For u = 2 they give 10 and 7: different, so they are not equal. Similarly 10y − 3 ≠ 10(y − 3). But 4(x + y) − y = 4x + 4y − y = 4x + 3y for every x and y. Equal expressions must agree for every value.

4(x + y) − y = 4x + 3y

Explore: sort like terms.

1. Put each term in its group of like terms.

Remember

• Add like terms by adding their numbers (5c + 3c = 8c); unlike terms stay separate.
• Open brackets with the usual sign rules, then group like terms; check by trying values.

Quick check

Simplify: 7p − p + 5q − 2q

1. 6p + 3q
2. 7p + 3q
3. 6p + 7q
4. 9pq

Think about it

One quiz player scores 21p − 9q and another 23p − 7q (p for a right answer, q a penalty). How much more did the second score?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.