## Answers

#### Explanation:

Note that:

#(a-b)^2 = a^2-2ab+b^2#

So putting

#497^2 = (500-3)^2#

#color(white)(497^2) = 500^2-2(500)(3)+3^2#

#color(white)(497^2) = 250000-3000+9#

#color(white)(497^2) = 247009#

Similarly, if we wanted to find

#(a+b)^2 = a^2+2ab+b^2#

to find:

#503^2 = (500+3)^2#

#color(white)(503^2) = 500^2+2(500)(3)+3^2#

#color(white)(503^2) = 250000+3000+9#

#color(white)(503^2) = 253009#

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