Question

Find the squares of the following numbers using the identity $a+b{)}^2=a^2+2ab+b^2$

(i) 405 (ii) 510
(iii) 1001 (iv) 209
(v) 605

Answer 1

$(a+b{)}^2=a^2+2ab+b^2$

(i) $(405{)}^2=(400+5{)}^2$
=$(400{)}^2+2\times 400\times 5+(5{)}^2$
=160000+4000+25
=164025

(ii) $(510{)}^2=(500+10{)}^2$
=$(500{)}^2+2\times 500\times 10+(10{)}^2$
=250000+10000+100
=260100

(iii) $(1001{)}^2=(1000+1{)}^2$
=$(1000{)}^2+2\times 1000\times 1+(1{)}^2$
=1000000+2000+1
=1002001

(iv) $(209{)}^2=(200+9{)}^2$
=$(200{)}^2+2\times 200\times 9+(9{)}^2$
=40000+3600+81
​​​​​​​=43681

(v) $(605{)}^2=(600+5{)}^2$
=$(600{)}^2+2\times 600\times 5+(5{)}^2$
=360000+6000+25​​​​​​​
=366025