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Question
Multiply: x2 + 4y2 + z3 + 2xy + xz − 2yz by x − 2y − z
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Solution
The given expression is
x2 + 4y2 + z3 + 2xy + xz − 2yz
We have to multiply the above expression by. `(x-2y -z)`
The required product is
`(x-2y-z)(x^2 +4y^2 +z^2+2xy+ xz - 2yz)`
` = {x + (-2y)+(-z)}{(x)^2 +(-2y)^2 + (-z)^2 -x.(-2y) - (-2y).(-z) - (-z).x}`
Recall the formula
`a^3 +b^3 +c^3 -3abc = (a+b+c)(a^2 +b^2 +c^2 - ab - bc - ca)`
Using the above formula, we have
` = x^3 + ( -2y)^3 + (-z)^3 -3.x.(-2y).(-z)`
` = x^3 -8y^3 - z^3 - 6xyz`
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