Multiply the binomials.

Question

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​
(
2
x
+
1
)
(
3
x
+
2
)
(2x+1)(3x+2)

Answer 1

To multiply the binomials \((2x + 1)(3x + 2)\), we can apply the distributive property (also known as the FOIL method for binomials):

1. First, multiply the first terms:
   \(2x \cdot 3x = 6x^2\)

2. Next, multiply the outer terms:
   \(2x \cdot 2 = 4x\)

3. Then, multiply the inner terms:
   \(1 \cdot 3x = 3x\)

4. Finally, multiply the last terms:
   \(1 \cdot 2 = 2\)

Now, combine all these results:
\[ 6x^2 + 4x + 3x + 2 \]

Combine the like terms (4x and 3x):
\[ 6x^2 + 7x + 2 \]

Therefore, the product of the binomials \((2x + 1)(3x + 2)\) is:
\[ \boxed{6x^2 + 7x + 2} \]