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3 years ago

Prove 151^3-25^3 is divisible by 126

Mathematics

1 answer:

stiks02 [169]3 years ago

4 0

9514 1404 393

Answer:

151 -25 = 126 is a factor of the difference of those cubes

Step-by-step explanation:

The expression can be factored as ...

a^3 -b^3 = (a -b)(a^2 +ab +b^2)

151^3 -25^3 = (151 -25)(151^2 +151·25 +25^2)

= 126(151^2 +151·25 +25^2)

That is, 126 is a factor of the difference of the given cubes. The difference is divisible by 126.

Your calculator tells you 151^3 -25^3 = 126 · 27201.

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