To multiply the polynomials \( (2x + 3)(3x + 2) \), we can use the distributive property (also known as the FOIL method for binomials).
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First: Multiply the first terms: \[ 2x \cdot 3x = 6x^2 \]
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Outer: Multiply the outer terms: \[ 2x \cdot 2 = 4x \]
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Inner: Multiply the inner terms: \[ 3 \cdot 3x = 9x \]
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Last: Multiply the last terms: \[ 3 \cdot 2 = 6 \]
Now, combine all these results: \[ 6x^2 + 4x + 9x + 6 \]
Next, combine the like terms (\(4x\) and \(9x\)): \[ 6x^2 + (4x + 9x) + 6 = 6x^2 + 13x + 6 \]
So, the final answer in standard form is: \[ \boxed{6x^2 + 13x + 6} \]