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Find the product: (a-b-c)(a^2+b^2+c^2+a ...

Find the product: `(a-b-c)(a^2+b^2+c^2+a b+a c-b c)`

Text Solution

Verified by Experts

We know that
`(x+y+z)(x^2+y^2+z^2−xy−yz−zx=x^3+y^3+z^3−3xyz`
Comparing both, we get
`x=a,y=b and z=c`
Then, `(a+(-b)+(-c))[(a)^2+(-b)^2+(-c)^2-(a)(-b)-(-b)(-c)-(a)(-c)]`
`=a^3+(-b)^3+(-c)^3−3(a)(-b)(-c)`
`=a^3-b^3-c^3−3abc`
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