Question

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

\\((x + 6)(x + 8)\\)

Explanation:

Identify the given expression

We are given two binomials to multiply:

$$(x + 6)(x + 8)$$

Apply the FOIL method

Using the FOIL Method, 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:

$$x \cdot 8 = 8x$$

• Inner: Multiply the inner terms:

$$6 \cdot x = 6x$$

• Last: Multiply the last terms of each binomial:

$$6 \cdot 8 = 48$$

Summing these terms gives:

$$x^2 + 8x + 6x + 48$$

Combine like terms

Using Polynomial Simplification, we group and combine the like terms, which are the linear \(x\) terms:

$$8x + 6x = (8 + 6)x = 14x$$

Substituting this back into our expression yields the final simplified polynomial:

$$x^2 + 14x + 48$$

Answer:

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

$$(x + 6)(x + 8) =$$

<blank>\(x^2 + 14x + 48\)</blank>