Question

Find the value of (55)^3 - (25)^3 - (30)^3.

Answer 1

Here,
55-25-30=0
Put the identity
if a+b+c=0
then,
${a}^{3} + {b}^{3} + {c}^{3} = 3abc$
Here,
$3 \times 55 \times 25 \times 30 = 123750$
That's your answer!
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Answer 2

Let a = 55, b = -25, c = -30

Then, a + b + c = 55 - 25 - 30 = 0

⇒a³ + b³ + c³ = 3abc

⇒ (55)³ + (-25)³ + (-30)³

⇒ 3(55) (-25) (-30)

⇛ 123750

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