NCERT Solutions Ganita Prakash (Part 1) Chapter 6 .2 Special Cases of the Distributive Property — In-text Questions
Book page 1456 Updated on2026-09-05
Q1.
The area of a square of sidelength 60 units is 3600 sq. units (60²) and that of a square of sidelength 5 units is 25 sq. units (5²). Can we use this to find the area of a square of sidelength 65 units?
Answer
Yes, but 3600 + 25 is not enough — two rectangles are missing.
Why it happens: stretching a square in both directions adds a strip along the right, a strip along the bottom, and the little corner square where the two strips meet. The two strips are the “2ab”; forgetting them is the commonest mistake in this chapter.
Q2.
Can you find the areas of the four parts in the figure above?
Answer
Part
Dimensions
Area (sq. units)
Large square
60 × 60
3600
Right rectangle
60 × 5
300
Bottom rectangle
5 × 60
300
Small square
5 × 5
25
Total
65 × 65
4225
3600 + 300 + 300 + 25 = 4225 ✓
Q3.
What if we write 65² as (30 + 35)² or (52 + 13)²? Draw the figures and check the area that you get.
Answer
The cut is in a different place, but the four pieces still add up to 4225.
65² split as (30 + 35)². The four areas 900, 1050, 1050 and 1225 again total 4225.
Why it happens: the square has one area, however you slice it. So every split gives a different-looking sum with the same total — which is exactly why (a + b)² = a² + 2ab + b² holds for all a and b, not just for 60 and 5.
Q4.
If a and b are any two integers, is (a + b)² always greater than a² + b²? If not, when is it greater?
Answer
No, not always. The difference between the two is the cross term.
(a + b)² – (a² + b²) = 2ab
Case
2ab
Conclusion
a, b same sign (both + or both –)
positive
(a + b)² > a² + b²
a = 0 or b = 0
zero
(a + b)² = a² + b²
a, b opposite signs
negative
(a + b)² < a² + b²
Examples: a = 3, b = 4 → 49 > 25. a = –3, b = –4 → 49 > 25. a = 3, b = –4 → 1 < 25. a = 5, b = 0 → 25 = 25.
Why it happens: for whole numbers a rectangle of area ab is really there twice, so the square of the sum must be bigger. When the signs disagree the two rectangles carry a minus sign and eat into the total instead.
Q5.
Use Identity 1A to find the values of 104², 37². (Hint: Decompose 104 and 37 into sums or differences of numbers whose squares are easy to compute.)
Check it yourself: 37 can also be split as 40 – 3, which needs Identity 1B: 1600 – 240 + 9 = 1369 — the same answer. Choose whichever split makes the two squares easiest.