Calculators are for the lazy II

Algebra Level 3

Compute 9 1 3 3 × 9 1 2 + 3 × 91 1 91^3-3\times91^2+3\times91-1 without a calculator.


Try Part I


The answer is 729000.

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2 solutions

Aaron Tsai
Jun 5, 2016

Let x = 91 x=91 and y = 1 y=1 . Then,

9 1 3 3 × 9 1 2 + 3 × 91 1 91^3-3\times91^2+3\times91-1

= x 3 3 x 2 y + 3 x y 2 y 3 = x^3-3x^2y + 3xy^2 - y^3

= ( x y ) 3 = (x-y)^3

Since x = 91 x=91 and y = 1 y=1 ,

( x y ) 3 = 9 0 3 = 729000 (x-y)^3=90^3=\boxed{729000}

nice solution, did the same.

Hana Wehbi - 5 years ago

Nice solution.+1! Did the same!

Rishabh Tiwari - 5 years ago
Hung Woei Neoh
Jun 5, 2016

Let a = 91 a=91 . We have:

9 1 3 3 × 9 1 2 + 3 × 91 1 = a 3 3 a 2 + 3 a 1 = ( a 1 ) 3 = ( 91 1 ) 3 = 9 0 3 = 729000 91^3 - 3 \times 91^2 + 3 \times 91 -1\\ =a^3 - 3a^2 + 3a - 1\\ =(a-1)^3\\ =(91-1)^3\\ =90^3 =\boxed{729000}

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