What must be added to #81x^2 - 72x + 9# to make it a perfect square?

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Answer 1 · 2016-03-31T22:01:04

A constant solution would be #7#

Another solution is #18x#

#81x^2-72x+9+7 = 81x^2-72x+16 = (9x-4)^2#

#81x^2-72x+9+18x = 81x^2-54x+9 = (9x-3)^2#

In general,

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

In the above solutions, we choose to change the constant term to match the #-2ab# term or the #-2ab# term to match the #b^2# term.