Question

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

\\((x - 6)(x + 4)\\)

Explanation:

Identify the given expression

We are given the product of two binomials:

$$ (x - 6)(x + 4) $$

Apply the FOIL method

Using the FOIL Method for Polynomial Multiplication, we multiply the terms in order: First, Outer, Inner, Last.

• First: Multiply the first terms of each binomial:

$$ x \cdot x = x^2 $$

• Outer: Multiply the outer terms:

$$ x \cdot 4 = 4x $$

• Inner: Multiply the inner terms:

$$ -6 \cdot x = -6x $$

• Last: Multiply the last terms:

$$ -6 \cdot 4 = -24 $$

Write the expanded expression

Combine the four resulting terms into one expression:

$$ x^2 + 4x - 6x - 24 $$

Combine like terms

Identify and combine the linear \(x\) terms:

$$ 4x - 6x = -2x $$

Thus, the simplified polynomial is:

$$ x^2 - 2x - 24 $$

Answer:

Multiply the binomials using the FOIL method. Combine like terms.

$$(x-6)(x+4) =$$

<blank>\(x^2 - 2x - 24\)</blank>