Evaluate by algebraic expansion of factorisation

Question

Evaluate the following by algebraic expansion of factorisation .

a) $2007^2$

b) $(503)(497)$

c) $20.5^2 - 19.5^2$

I'm not sure what does it mean by "algebraic expansion of factorisation ." Can I get help please. Thanks in advance !

Answer 1

$$2007^2=(2000+7)^2=2000^2+14\cdot 2000+49=4000000+28000+49=4028049$$ $$503\cdot 497=(500+3)(500-3)=500^2-3^2=250000-9=249991$$ $$20.5^2-19.5^2=(20.5-19.5)(20.5+19.5)=1\cdot 40=40$$