Question

Multiply. Express your answer as a polynomial in standard form.

(2x+3)(3x+2)

(1 point)
Responses

6x2+13x + 6
6x2+13x + 6

5x2+13x + 5
5x2+13x + 5

6x2+ 6
6x2+ 6

None of the above

Answer 1

To multiply the polynomials \((2x + 3)(3x + 2)\), we can use 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: \(3 \cdot 3x = 9x\)
4. 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:

\[
\boxed{6x^2 + 13x + 6}
\]