NCERT Book Class 8 Mathematics (Part I) Chapter 6 We Distribute, Yet Things Multiply

WE DISTRIBUTE,
6 YET THINGS
MULTIPLY

We have seen how algebra makes use of letter symbols to write general
statements about patterns and relations in a compact manner. Algebra
can also be used to justify or prove claims and conjectures (like the many
properties you saw in the previous chapter) and to solve problems of
various kinds.
Distributivity is a property relating multiplication and addition that
is captured concisely using algebra. In this chapter, we explore different
types of multiplication patterns and show how they can be described in
the language of algebra by making use of distributivity.

6.1 Some Properties of Multiplication
Increments in Products
Consider the multiplication of two numbers, say, 23 × 27.

1. By how much does the product increase if the first number (23) is
increased by 1?

2. What if the second number (27) is increased by 1?

3. How about when both numbers are increased by 1?

Do you see a pattern that could help generalise our observations to the
product of any two numbers?
Let us first consider a simpler problem — find the increase in the
product when 27 is increased by 1. From the definition of multiplication
(and the commutative property), it is clear that the product increases by
23. This can be seen from the distributive property of multiplication as
well. If a, b and c are three numbers, then —