Questions: Find the product. (x+2)(x+3) (x+2)(x+3)= (Simplify your answer. Use integers or decimals for any numbers

Find the product. (x+2)(x+3) (x+2)(x+3)= (Simplify your answer. Use integers or decimals for any numbers
Transcript text: Find the product. \[ \begin{array}{l} (x+2)(x+3) \\ (x+2)(x+3)= \end{array} \] (Simplify your answer. Use integers or decimals for any numbers
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Solution

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Solution Steps

Step 1: Define the Binomials

We start with the binomials \( (x + 2) \) and \( (x + 3) \).

Step 2: Apply the Distributive Property

Using the distributive property (FOIL method), we multiply each term in the first binomial by each term in the second binomial: \[ (x + 2)(x + 3) = x \cdot x + x \cdot 3 + 2 \cdot x + 2 \cdot 3 \]

Step 3: Combine Like Terms

Now, we combine the like terms from the expansion: \[ x^2 + 3x + 2x + 6 = x^2 + 5x + 6 \]

Final Answer

The product of the binomials is \[ \boxed{x^2 + 5x + 6} \]

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