Question

multiply the binomials using the foil method. combine like terms.

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

Explanation:

Identify the given expression

We are given two binomials to multiply:

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

Apply the FOIL method

We will use the FOIL Method to multiply the binomials. FOIL stands for:

• First: Multiply the first terms of each binomial.
• Outer: Multiply the outer terms.
• Inner: Multiply the inner terms.
• Last: Multiply the last terms.

Applying this to our expression:

• First: \(x \cdot x = x^2\)
• Outer: \(x \cdot 2 = 2x\)
• Inner: \(3 \cdot x = 3x\)
• Last: \(3 \cdot 2 = 6\)

This gives us:

$$x^2 + 2x + 3x + 6$$

Combine like terms

Now, we simplify the expression using Polynomial Simplification by combining the like terms, which are the linear terms \(2x\) and \(3x\):

$$2x + 3x = (2 + 3)x = 5x$$

Substituting this back into our expression yields:

$$x^2 + 5x + 6$$

Answer:

\(x^2 + 5x + 6\)