Question

Show that
$15 {}^{3} + 8 {}^{3}$
Is divisible by 23.

Answer 1

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$a {}^{3} + b {}^{3} = (a - b)(a {}^{2} + ab + b {}^{2} )$
Therefore ,

15^3 + 8^3 = (15+8)(15^2-15×8+8^2)

=23(225-120+64)

=23×169

Therefore, Its divisible by 23.

Thanks!

Answer 2

   

We can prove it by factorization.

According to  a³ + b³ = (a + b)(a² - ab + b²),

$15^3+8^3 \\ \\ (15+8)(15^2-(15 \times 8) + 8^2) \\ \\ 23(225-120+64) \\ \\ 23\times 169$

So it's divisible by 23.

That's all!

Plz mark it as the brainliest.

Thank you. :-))