16. 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.

 

	48 54 60 56 63 70 64 72 80   $6·8$ $6·9$ $6·10$ $7·8$ $7·9$ $7·10$ $8·8$ $8·9$ $8·10$

 

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

 

 Answer:

 

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