Question

Find the square of the following without actual multiplication

Answer 1

(1)-

(39)²

=> (39)²

=> (40-1)²
==============
By formula,
(a-b)²=a²+b²-2ab
==============

=> (40-1)²

=> (40)²+(1)²-2[40×1]

=> 1600 + 1 -80

=> 1521

_____________________

(2)-

42²

=> (42)²

=> (40+2)²
==================
By formula,
(a+b)²=a²+b²+2ab
==================

=> (40+2)²

=> (40)²+(2)²+2[40×2]

=> 1600+4+160

=> 1764

______________________

(3)-

93²

=> (93)²

=> (100-7)²
==================
By formula,
(a-b)²=a²+b²-2ab
===================

=> (100-7)²

=> (100)²+(7)² -2[7×100]

=> 10000+49-1400

=> 8649

_______________________

(4)-

71²

=> (71)²

=> (70+1)²
=====================
By formula,
(a+b)²=a²+b²+2ab
=====================

=> (70+1)²

=> (70)²+(1)²+2[70×1]

=> 4900+1+140

=> 5041

______________________

(5)-

46²

=> (46)²

=> (40+6)²
===================
By formula,
(a+b)²=a²+b²+2ab
===================

=> (40+6)²

=> (40)²+(6)²+2[40×6]

=> 1600+36+480

=> 2116


I hope this will help you



-by ABHAY