Question

express the volume of the cube in 2k-1×2k-1×2k-1​

Answer 1

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Given that:

Side=2k-1

To Find:

volume of the cube

Formula used : volume of the cube= side³

Solution:

volume of the cube= side³

Side=2k-1

Then, Side³= (2k-1)³

(2k-1)³ :.[ (a-b)³=a³-b³-3ab(a-b)]

(2k-1)³= (2k)³-(1)³-3×2k×1(2k-1)

(2k-1)³= 8k³-1-6k(2k-1)

(2k-1)³= 8k³-1-12k+6k

(2k-1)³= 8k³-1-6k

(2k-1)³= 8k³-6k-1

Answer:

(2k-1)³= 8k³-6k-1

So, volume of the cube= 8k³-6k-1