Know your 123s

Algebra Level 1

Evaluate

32 1 2 − 12 3 2 321 − 123 . \frac{ 321 ^2 - 123 ^2 } { 321 - 123} .


The answer is 444.

Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

Using the algebraic identity ( a 2 − b 2 ) = ( a − b ) ( a + b ) (a^2-b^2) = (a-b)(a+b) , we see that a 2 − b 2 a − b = a + b \frac{a^2 - b^2}{a-b} = a+b .

Substituting in a = 321 , b = 123 a = 321, b = 123 , we get that

32 1 2 − 12 3 2 321 − 123 = 321 + 123 = 444. \frac{ 321^2 - 123^2 } { 321 - 123} = 321 + 123 = 444.

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