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  • Find the following product (2x-y+3z)(4x^{2}+y^{2}+9z^{2}+2xy+3yz-6xz)

Find the following product (2x-y+3z)(4x^{2}+y^{2}+9z^{2}+2xy+3yz-6xz)

Answers (1)

8x^{3}-y^{3}+27x^{3}

Solution

Given:  (2x-y+3z)(4x^{2}+y^{2}+9z^{2}+2xy+3yz-6xz)

This can be written as

(2x-y+3z)((2x)^{2}+(y)^{2}+(3z)^{2}-(2x)(-y)-(-y)(3z)-(2x)(3z))

We know that

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

Comparing equation (i) with the above identity we get:

a = 2x, b = -y, c = 3z

Hence,

(2x-y+3z)((2x)^{2}+(y)^{2}+(3z)^{2}-(2x)(-y)-(-y)(3z)-(2x)(3z))\\ =(2x)^{3}+(-y)^{3}+(3z)^{3}-3(2x)(-y)(3z)\\ =8x^{3}-y^{3}+27z^{3}+18xyz

Posted by

infoexpert24

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