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)^2\\)

Explanation:

Identify the appropriate special product

We are given the expression \((x + 9)^2\). This expression represents a binomial multiplied by itself, specifically in the form of a sum. We can apply the Square of a Binomial Sum formula, which is a key type of Special Products:

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

Match the terms of the binomial

Let's identify the terms \(a\) and \(b\) from our given expression \((x + 9)^2\):

• The first term is \(a = x\)
• The second term is \(b = 9\)

Apply the algebraic expansion formula

Now, we substitute \(a = x\) and \(b = 9\) into the expansion formula:

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

Simplify each term of the polynomial

We simplify each part of the expanded expression:

• The first term is \(x^2\)
• The middle term is \(2 \cdot x \cdot 9 = 18x\)
• The last term is \(9^2 = 81\)

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).

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

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