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Question
Find the following product:
(3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
Solution
In the given problem, we have to find Product of equations
Given (3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)
We shall use the identity
`x^3 + y^3 + z^3 - 3xyz = (x+y+z) (x^2 + y^2 + z^2 - xy - yz - zx)`
` = (3x)^3 + (2y)^3 + (2z)^3 - 3 (3x)(2y)(2z)`
` =(3x) xx (3x) xx (3x) + (2y) xx(2y) xx(2y) + (2z) xx(2z) xx(2z)-3(3x)(2y)(2z) `
` = 27x^3 + 8y^3 + 8z^3 - 36xyz`
Hence the product of (3x + 2y + 2z) (9x2 + 4y2 + 4z2 − 6xy − 4yz − 6zx)is `27x^3 + 8y^3 + 8z^3 - 36xyz`
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