1 answer

How do you use a special product of "algebraic expression" to evaluate a number?e.g 497 square

Question:

How do you use a special product of "algebraic expression" to evaluate a number?e.g 497 square

Answers

#497^2 = (500-3)^2# so can use #(a-b)^2 = a^2-2ab+b^2#

Explanation:

Note that:

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

So putting #a=500# and #b=3#, we find:

#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 #503^2# we could use:

#(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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