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Question

Find the product:
(x+2y+3z)(x2+4y2+9z2−2xy−6yz−3zx)

A
x3+8y3+27z3+18xyz
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B
x3+8y3+27z318xyz
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C
x3+8y327z318xyz
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D
x38y3+27z318xyz
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Solution

The correct option is B x3+8y3+27z318xyz
Identity used: x3+y3+z33xyz=(x+y+z)(x2+y2+z2xyyzzx)
Now,(x+2y+3z)(x2+4y2+9z22xy6yz3zx)
=(x+2y+3z)(x2+(2y)2+(3z)2x×2y2y×3z3z×x)
=x3+(2y)3+(3z)23×x×2y×3z
=x3+8y3+27z318xyz

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