11. NCERT | Distributivity | Figure It Out | Pg.142 | Q1

Observe the multiplication grid below. Each number inside the grid is formed by multiplying two numbers. If the middle number of a \(3 × 3\) frame is given by the expression \(pq\), as shown in the figure, write the expressions for the other numbers in the grid.

 

	8 9 10 16 18 20 24 27 30   $1·8$ $1·9$ $1·10$ $2·8$ $2·9$ $2·10$ $3·8$ $3·9$ $3·10$

 

[Note: Consider the exact match of given \(3 \times 3\) grid.]

 

 Answer:

 

p(q-1)(p+1)(q-1)(p-1)(q-1)	(p+1)q(p-1)qpq	(p+1)(q+1)p(q+1)(p-1)(q+1)
(p+1)(q-1)p(q-1)(p-1)(q-1)	\(pq\)	p(q+1)(p-1)(q+1)(p+1)(q+1)
(p+1)(q-1)(p-1)(q-1)p(q-1)	(p+1)qpq(p-1)q	(p-1)(q+1)p(q+1)(p+1)(q+1)