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Simplify: (6m-n)(36 m^2+6m m+n^2)-(3m+2n...

Simplify: `(6m-n)(36 m^2+6m m+n^2)-(3m+2n)^3`

Text Solution

Verified by Experts

Solution:
`(6m−n)(36m^2 +6mn+n^2 )−(3m+2n)^3`
Using identity
`a^3-b^3=(a-b)(a^2+b^2-ab)`
`=(6m−n)[(6m)^2+6m×n+(n)^2 ]−(3m+2n)^3`
`=[(6m)^3−n^3 ]−[(3m)^3+(2n)^3 +3×3m×2n(3m+2n)]`
`=(216m^3−n^3)−(27m^3+8n^3+54m^2n+36mn^2)=216m^3 −n^3−27m^3−8n^3 −54m^2 n−36mn^2`
`=189m^3−9n^3−54m^2n−36mn^2`
Hence the answer is
`189m^3−9n^3−54m^2n−36mn^2`
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