NCERT Solutions Ganita Prakash (Part 1) Chapter 6 .1 Some Properties of Multiplication — In-text Questions
Book page 1396 Updated on2026-09-05
Q1.
By how much will the product of two numbers change if one of the numbers is increased by m and the other by n?
Answer
The two numbers become a + m and b + n, and the product changes by an + bm + mn.
(a + m)(b + n) = (a + m) b + (a + m) n = ab + mb + an + mn Identity 1: (a + m)(b + n) = ab + mb + an + mn
Subtracting the old product ab leaves the change: an + bm + mn.
An (a + m) by (b + n) array of dots splits into four blocks. Their counts ab, an, mb, mn are the four terms of Identity 1.
Why it happens: the product is the sum of the product of each term of (a + m) with each term of (b + n). That is all “expanding a bracket” ever means, and it is just distributivity used twice.