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 pattern

We need to find the product of the binomials:

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

This matches the Difference of Squares special product formula.
Using the Difference of Squares and Special Products knowledge points:

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

Map the terms to the formula

Identify the terms \(a\) and \(b\) in our expression:

• Let \(a = x\)
• Let \(b = 9\)

Apply the formula

Substitute \(a\) and \(b\) into the difference of squares formula:

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

Simplify the expression

Calculate the square of 9:

$$ 9^2 = 81 $$

Thus, the simplified product is:

$$ x^2 - 81 $$

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).

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

Answer: <blank>\(x^2 - 81\)</blank>