What Algebraic Identities Are Needed?

Algebra Level 3

( 2 5 3 − 2 3 ) ( 4 25 3 + 2 10 3 + 4 3 ) = ? \large \left( 2\sqrt [ 3 ]{ 5 } -\sqrt [ 3 ]{ 2 } \right) \left( 4\sqrt [ 3 ]{ 25 } +2\sqrt [ 3 ]{ 10 } +\sqrt [ 3 ]{ 4 } \right) = \, ?


The answer is 38.

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Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Ashish Menon
Mar 24, 2016

The question is of the form ( a − b ) ( a 2 + a b + b 2 ) (a-b)(a^2 + ab + b^2) which is the the expansion of a 3 − b 3 a^3 - b^3
Substituting the values, we get:-
( 2 5 3 ) 3 − ( 2 3 ) 3 {(2\sqrt[3]{5})}^3 - {(\sqrt[3]{2})}^3
= ( 8 × 5 ) − 2 (8×5) - 2
= 40 − 2 40 - 2
= 38 38 . □ _\square


28 Helpful 1 Interesting 1 Brilliant 0 Confused

Moderator note:

Good observation about the substitution of a a and b b .

brilliant ashish Siva

Arun Garg - 5 years, 2 months ago

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Thanks arun :-)

Ashish Menon - 5 years, 2 months ago

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