Question

Simplify:
(x + 2y + 3z)(x² + 4y² + 9z² - 2xy - 6yz - 3zx)

Answer 1

(x + 2y + 3z)(x² + 4y² + 9z² - 2xy - 6yz - 3zx)
= x(x² + 4y² + 9z² - 2xy - 6yz - 3zx) + 2y(x² + 4y² + 9z² - 2xy - 6yz - 3zx)
= x³ + 4xy² + 9xz² - 2x²y - 6xyz - 3zx² + 2x²y + 8y³ + 18yz² - 4xy² - 12²z - 6xyz + 3x²z + 12y²z + 27z³ - 6xyz - 18yz² - 9xz²
= x³ + 8y³ + 27z³ - 18xyz.