Multiply:$x^2 + 4y^2 + z^2 + 2xy + xz - 2yz$ by $x- 2y-z$


Given:

$x^2 + 4y^2 + z^2 + 2xy + xz - 2yz$ by $x- 2y-z$

To do:

We have to multiply the given expressions.

Solution:

We know that,

$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$

Therefore,

$(x^2 + 4y^2 + z^2 + 2xy + xz - 2yz) \times (x - 2y - z) = (x -2y-z) [x^2 + (-2y)^2 + (-z)^2 -x \times (- 2y) - (-2y)\times (z) - (-z) \times (x)]$

$= x^3 + (-2y)^3 + (-z)^3 - 3x (-2y) (-z)$

$= x^3 - 8y^3 - z^3 - 6xyz$

Hence, $(x^2 + 4y^2 + z^2 + 2xy + xz - 2yz) \times (x - 2y - z) = x^3 - 8y^3 - z^3 - 6xyz$.

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Updated on: 10-Oct-2022

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