Find the number of unlike terms in (x + 2y + 3z)(2x - y + z).
6
Multiplying out \((x + 2y + 3z)(2x - y + z)\) term by term:
\(x(2x - y + z) = 2x^2 - xy + xz\)
\(2y(2x - y + z) = 4xy - 2y^2 + 2yz\)
\(3z(2x - y + z) = 6xz - 3yz + 3z^2\)
Adding and combining like terms: \(2x^2 - 2y^2 + 3z^2 + 3xy + 7xz - yz\).
This simplified expression has 6 unlike terms.
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