- 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 represented by the expression pq, as shown in the figure, write the algebraic expressions for the remaining eight numbers in the 3×3 frame. Simplify your answers wherever possible.
Solution:-
Let the middle number of the 3×3 frame be pq.
This means:
- The middle cell is formed by multiplying p and q.
- Therefore, the row numbers are:
- Top row: p−1
- Middle row: p
- Bottom row: p+1
- The column numbers are:
- Left column: q−1
- Middle column: q
- Right column: q+1
pq − p − q + 1 | pq − q | pq − p + q − 1 |
pq − p | pq | pq + p |
pq + p − q − 1 | pq + q | pq + p + q + 1 |
Question 2. Expand the following products.
(i) (3+u)(v-3)
Solutions: (3+u)(v-3) = 3(v-3) +u(v-3)
= 3v – 9 + uv – 3u
(ii) 2/3(15 + 6a)
Solutions: 2/3 (15 + 6a)
= 2/3 x 15 + 2/3 x 6a
= 10 + 4a
(iii)(10a+b)(10c+d)
Solutions: 10 (10c+d) +b (10c+d)
= 100c + 10d + 10 bc + bd
(iv) (3-x) (x-6) = 3 (x – 6 ) – x (x – 6)
= 3x – 18 – $$x^{2}$$ -6x