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

Given:

$x^2 +y^2 + z^2 - xy + xz + yz$ and $x + y - z$

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,

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

$=x^3 +y^3 - z^3 + 3xyz$

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

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Updated on: 10-Oct-2022

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