Question
Simplify:$(x + 2y + 3z)(x^2 + 4y^2 + 9z^2 - 2xy - 6yz - 3zx)$
✓
Answer
$(x + 2y + 3z)(x^2 + 4y^2 + 9z^2 - 2xy - 6yz - 3zx)$
$= x(x^2 + 4y^2 + 9z^2 - 2xy - 6yz - 3zx) + 2y(x^2+ 4y^2 + 9z^2 - 2xy - 6yz - 3zx)$
$= x^3 + 4xy^2 + 9xz^2 - 2x^2y - 6xyz - 3zx^2 + 2x^2y $$+ 8y^3 + 18yz^2 - 4xy^2 - 12^2z - 6xyz + 3x^2z + 12y^2z + 27z^3 - 6xyz - 18yz^2 - 9xz^2$
$= x^3+ 8y^3 + 27z^3 - 18xyz.$
$= x(x^2 + 4y^2 + 9z^2 - 2xy - 6yz - 3zx) + 2y(x^2+ 4y^2 + 9z^2 - 2xy - 6yz - 3zx)$
$= x^3 + 4xy^2 + 9xz^2 - 2x^2y - 6xyz - 3zx^2 + 2x^2y $$+ 8y^3 + 18yz^2 - 4xy^2 - 12^2z - 6xyz + 3x^2z + 12y^2z + 27z^3 - 6xyz - 18yz^2 - 9xz^2$
$= x^3+ 8y^3 + 27z^3 - 18xyz.$
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