Question

find the product of the binomials using the appropriate special product (difference of two squares, square of a binomial sum, or square of a binomial difference).

\\((x + 9)(x + 9)\\)

Explanation:

Identify the special product type

We are given the expression:

$$ (x + 9)(x + 9) $$

This is the product of a binomial with itself, which can be written as:

$$ (x + 9)^2 $$

This matches the Square of a Binomial Sum pattern.

Recall the special product formula

The formula for the Square of a Binomial Sum is:

$$ (a + b)^2 = a^2 + 2ab + b^2 $$

In our expression, we identify:

• \( a = x \)
• \( b = 9 \)

Apply the formula to expand

Using the Special Products formula, we substitute \( a = x \) and \( b = 9 \):

$$ (x + 9)^2 = (x)^2 + 2(x)(9) + (9)^2 $$

Simplify each term

We calculate each part of the expanded expression:

• First term: \( x^2 \)
• Middle term: \( 2 \cdot 9 \cdot x = 18x \)
• Last term: \( 9^2 = 81 \)

Combining these terms gives:

$$ x^2 + 18x + 81 $$

Answer:

Find the product of the binomials using the appropriate special product (difference of two squares, square of a binomial sum, or square of a binomial difference).

$$ (x + 9)(x + 9) = $$

<blank>\(x^2 + 18x + 81\)</blank>