Question:
Evaluate
(i) $(99)^{2}$
(ii) $(995)^{2}$
(iii) $(107)^{2}$
Solution:
(i) $(99)^{2}=(100-1)^{2}$
$=[(100)+(-1)]^{2}$
$=(100)^{2}+2 \times(100) \times(-1)+(-1)^{2}$
$=10000-200+1$
$=9801$
(ii) $(995)^{2}=(1000-5)^{2}$
$=[(1000)+(-5)]^{2}$
$=(1000)^{2}+2 \times(1000) \times(-5)+(-5)^{2}$
$=1000000-10000+25$
$=990025$
(iii) $(107)^{2}=(100+7)^{2}$
$=(100)^{2}+2 \times(100) \times(7)+(7)^{2}$
$=10000+1400+49$
$=11449$
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