Simplify the given mathematical expression:
$2 (3 x^{2} + 5 x - 9) - (x^{2} + 2 x + 6)$

Answer

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Answer

Final Answer: The simplified expression is $5 x^{2} + 8 x - 24$

Steps

Step 1 ：Distribute the 2 in the first parentheses: $2 * (3 x^{2} + 5 x - 9) = 6 x^{2} + 10 x - 18$

Step 2 ：Subtract the second parentheses from the result: $6 x^{2} + 10 x - 18 - (x^{2} + 2 x + 6) = 5 x^{2} + 8 x - 24$

Step 3 ：Final Answer: The simplified expression is $5 x^{2} + 8 x - 24$