What is the most simplified expression for 4 c squared d plus 3 d c minus 2 times open paren d c squared plus c d close paren plus 6 c squared d squared ?

Distribute −2 across the parentheses: −2(dc² + cd) = −2dc² − 2cd. Since dc² is the same as c²d, combine like terms: 4c²d − 2c²d = 2c²d, and 3dc − 2cd = dc. The term 6c²d² is unlike the others, so it stays as it is. The simplified expression is 2c²d + dc + 6c²d², which is choice C.

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