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Find the product: (2x-y+3z)(4x^2+y^2+9z...

Find the product: `(2x-y+3z)(4x^2+y^2+9z^2+2x y+3y z-6x z)`

Text Solution

Verified by Experts

Putting `2x=a,y=b and, 3z=c`, we get
`(2x-y+3z)(4x^2+y^2+9z^2+2xy+3yz-6xz)`
`=[2x+(-y)+(3z)]xx[(2x)^2+(-y)^2+(3z)^2-(2x)(-y)-(-y)(3z)-(2x)(3z)]`
`=(a+b+c)xx(a^2+b^2+c^2-ab-bc-ca)`
`=a^3+b^3+c^3-3abc`
`=(2x)^3+(-y)^3+(3z)^3-3xx(2x)xx (-y)xx(3z)`
`=8x^-y^3+27z^3+18zyz`.
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