5. TBQ - Figure out the correct expresion

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.

 

	3 6 9 4 8 12 5 10 15   $3·1$ $3·2$ $3·3$ $4·1$ $4·2$ $4·3$ $5·1$ $5·2$ $5·3$

 

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