Question

Using the formula for squaring a binomial, evaluate the following:
(i) $(69{)}^2$
(ii) $(78{)}^2$
(iii) $(197{)}^2$
(iv) $(999{)}^2$

Answer 1

(i) $(69{)}^2=(70-1{)}^2=(70{)}^2-2\times 70\times 1+(1{)}^2=4900-140+1=4901-140=4761$

(ii) $(78{)}^2=(80-2{)}^2=(80{)}^2-2\times 80\times 2+(2{)}^2=6400-320+4=6404-320=6084$

(iii) $(197{)}^2=(200-3{)}^2=(200{)}^2-2\times 200\times 3+(3{)}^2=40000-1200+9=40009-1200=38809$

(iv) $(999{)}^2=(1000-1{)}^2=(1000{)}^2-2\times 1000\times 1+(1{)}^2=1000000-2000+1=1000001-2000=998001$