NCERT Solutions for Class 8th Maths Chapter 6 .2 Special Cases of the Distributive Property — In-text Questions
Book page 1456 Updated on2026-09-19
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?
Page 145 — a square of side 65 split into four parts, 60 + 5 along each side.
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.
The worked figure on page 145 — the square of side 65 split as 60 + 5.
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.