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Question
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
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Solution
In the given problem, we have to find Product of equations
Given (4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
We shall use the identity
`x^3 + y^3 + z^3 - 3xyz = (x+ y +z)(x^2 + y^2 + z^2 - xy - yz - zx)`
` = (4x)^3 + (3y)^3 + (2z)^3 -3 (4x)(3y)(2z)`
` = (4x) xx (4x) xx (4x) +(-3y) xx (-3y) xx (-3y) + (2z) xx (2z) xx (2z) -3 (4x) (-3y)(2z)`
` = 64x^3 - 27y^3 + 8z^3 + 72 xyz`
Hence the product of (4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx) is `64x^2 - 27y^3 + 8z^3 + 72xyz`
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