To multiply the polynomials \((2x + 3)(3x + 2)\), we can use the distributive property (also known as the FOIL method for binomials):
- First, multiply the first terms: \(2x \cdot 3x = 6x^2\)
- Next, multiply the outer terms: \(2x \cdot 2 = 4x\)
- Then, multiply the inner terms: \(3 \cdot 3x = 9x\)
- Lastly, multiply the last terms: \(3 \cdot 2 = 6\)
Now combine all these results:
\[ 6x^2 + 4x + 9x + 6 \]
Combine like terms (\(4x + 9x\)):
\[ 6x^2 + 13x + 6 \]
Thus, the answer expressed as a polynomial in standard form is:
\[ \boxed{6x^2 + 13x + 6} \]
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