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Factorize: a^3+8b^3+64 c^3-24 a b c...

Factorize: `a^3+8b^3+64 c^3-24 a b c`

Text Solution

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Given: `a^3+8b^3+64c^3-24abc`
`=a^3+(2b)^3+(4c)^3-3(a)(2b)(4c)`
we know,
`x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)`
so,
`=(a+2b+4c)[a^2+(2b)^2+(4c)^2-a(2b)-(2b)(4c)-(4c)a]`
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