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Multiply: x^2+4y^2+z^2+2x y+x z-2y z\ b...

Multiply: `x^2+4y^2+z^2+2x y+x z-2y z\ ` by `x-2y-z`

Text Solution

Verified by Experts

Putting `x=a,-2y=b and -z=c`, we get
`(x-2y-z)(x^2+4y^2+z^2+z^2+2xy-2yz+zx)`
`=[x+(-2y)+(-z)]xx[x^2+(-2y)^2+(-z)^2-x xx (-2y)-(-2y)xx(-z)-(-z)xx x]`
`=(a+b+c)xx (a^2+b^2+c^2-ab-bc -ca)`
`=a^3+b^3+c^2-3 abc`
`=x^3+(-2y)^3+(-z)^3 -3 xx x xx (-2y)xx(-z)`
`=x^3-8y^3-z^3-6xyz`.
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