Question

50 Points!

Answer 1

Answer:

327^3 = 34 965 783

173^3 = 5 177 717

34 965 783 + 5 177 717 = 40 143 500

40 143 500 ÷ 500 = 80 287

80 287 is a whole number, therefore, 327^3 + 173^3 is divisible by 500.

I hope this helps :)

Answer 2

Answer:

Step-by-step explanation:

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ALGEBRAIC IDENTITY USED IN THIS QUESTION :-

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

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Lets expand 327³ + 173³.

$=> (327 + 173)(327^2 + 173^2 - 327 \times 173)$

$=> 500 \times (327^2 + 173^2 - 327 \times 173)$

After expanding it , we get 500 & (327² + 173² - 327×173) as factors.

∴ Hence , 327³ + 173³ is divisible by 500.