Using the formula for squaring a binomial, evaluate the following:
(i) (102)2
(ii) (99)2
(iii) (1001)2
(iv) (999)2
(v) (703)2
(i) Here, we will use the identity $(a+b)^{2}=a^{2}+2 a b+b^{2}$
$(102)^{2}$
$=(100+2)^{2}$
$=(100)^{2}+2 \times 100 \times 2+2^{2}$
$=10000+400+4$
$=10404$
(ii) Here, we will use the identity $(a-b)^{2}=a^{2}-2 a b+b^{2}$
$(99)^{2}$
$=(100-1)^{2}$
$=(100)^{2}-2 \times 100 \times 1+1^{2}$
$=10000-200+1$
$=9801$
(iii) Here, we will use the identity $(a+b)^{2}=a^{2}+2 a b+b^{2}$
(1001) $^{2}$
$=(1000+1)^{2}$
$=(1000)^{2}+2 \times 1000 \times 1+1^{2}$
$=1000000+2000+1$
$=1002001$
(iv) Here, we will use the identity $(a-b)^{2}=a^{2}-2 a b+b^{2}$
$(999)^{2}$
$=(1000-1)^{2}$
$=(1000)^{2}-2 \times 1000 \times 1+1^{2}$
$=1000000-2000+1$
$=998001$
(v) Here, we will use the identity $(a+b)^{2}=a^{2}+2 a b+b^{2}$
(703) $^{2}$
$=(700+3)^{2}$
$=(700)^{2}+2 \times 700 \times 3+3^{2}$
$=490000+4200+9$
$=494209$