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  • Multiply: Multiply: x^{2}+4y^{2}+z^{2}+2xy+xz-2yz by \left ( -z+x-2y \right )

Multiply: x^{2}+4y^{2}+z^{2}+2xy+xz-2yz by \left ( -z+x-2y \right )

Answers (1)

x^{3}-8y^{3}-z^{3}-6xyz

Solution

We have, \left (x^{2}+4y^{2}+z^{2}+2xy+xz-2yz \right ) \left ( -z+x-2y \right )                  

This can be written as:

 \left ( x+(-2y)+(-z) \right )\left ((x)^{2}+(-2y)^{2}+(z)^{2}-(x)(-z)-(-z)(-2y)\right )\cdots \cdots (i)                                

 We know that

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

So comparing the RHS of equation (i) with the above identity:

a = x

b = -2y

 c = -z

We get:

\left ( x+(-2y)+(-z) \right )\left ((x)^{2}+(-2y)^{2}+(z)^{2}-(x)(-z)-(-z)(-2y)\right )\\ =(x)^{3}+(-2y)^{3}+(-z)^{3}-3(x)(-2y)(-z)\\ =x^{3}-8y^{3}-z^{3}-6xyz

Hence the answer is x^{3}-8y^{3}-z^{3}-6xyz.  

Posted by

infoexpert24

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