You are here
Computing Squares using Identity 1C
Last updated at January 13, 2026 by Teachoo
Class 8 (Ganita Prakash - 1, 2 & Old NCERT)
Chapter 6 Class 8 - We Distribute yet things Multiply (Ganita Prakash)
- Distributive Property
- Figure it out - Page 142, 143
- Fast Multiplications Using the Distributive Property
- Square of the Sum/Difference of Two Numbers
-
Investigating Patterns
- Figure it out - Page 149
- Mind the Mistake, Mend the Mistake
- This Way or That Way, All Ways Lead to the Bay
- Area of Shaded Region
- Figure it out - Page 154-156
Transcript
Computing Squares using Identity 1COur Identity 1C is a2 – b2 = (a + b) × (a – b) Putting b2 on left side a2 = (a + b) × (a – b) + b2 This was discovered by Sridharacharya (750 CE). It is useful to find squares of some numbers like 312, 1972 For 312 We take a = 31, b = 1 312 = (31 + 1) × (31 – 1) + 12 = 32 × 30 + 1 = 960 + 1 = 961 For 1972 We take a = 197, b = 3 (As 197 + 3 = 200 – so its easier to calculate) 1972 = (197 + 3) × (197 – 3) + 32 = 200 × 194 + 9 = 38,800 + 9 = 38,809 We use this method because Instead of muliplying two hard numbers like 197 × 197 We multiply easy number 200 with a hard number 194
