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Question
Find the following product:
(3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
Solution
In the given problem, we have to find Product of equations
Given (3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)
We shall use the identity
`x^3 + y^3 + z^3 -xyz = (x+ y +z)(x^2 + y^2+z^2 - xy - yz -zx)`
` = (3x)^3 + (-4y)^3 + (5z)^3 - 3 (3x)(4y) (5z)`
`= (3x)xx (3x)xx(3x) - (-4y) xx (-4y) xx (-4y)+(5z)xx (5z)xx(5z) -3 (3x) (-4y)(5z)`
` = 27x^3 - 64y^3 + 125z^3 + 180xyz`
Hence the product of (3x − 4y + 5z) (9x2 +16y2 + 25z2 + 12xy −15zx + 20yz)is ` 27x^3 - 64y^3 + 125z^3 + 180xyz`
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