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Algebra Level 2

Simplify:

$\frac{ 83^3 + 17^3 } { ( 83 \times 66) + 17^2 }$

2 solutions

Chew-Seong Cheong
Dec 7, 2014

Same logic but showing it with numbers only.

$\dfrac {83^3+17^3} {(83\times 66)+17^2} = \dfrac {(83+17)[83^2 - (83 \times 17) + 17^2]} {(83\times 66)+17^2}$

$= \dfrac {100[83(83-17)+17^2]} {(83\times 66)+17^2} = \dfrac {100[(83\times 66) +17^2]} {(83\times 66)+17^2} = \boxed {100}$

Christian Daang
Oct 26, 2014

let a= 83 and b = 17

Then, the expression is equal to:

(a^3 + b^3)/[(a)(a-b) + b^2]

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

= a+b

= 83 + 17 = 100

Final Answer: 100.