Question

question 1 of 11, step 1 of 1

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 + 2)^2\\

Explanation:

Identify the appropriate special product formula

We are asked to find the product of the binomial expression:

$$(x + 2)^2$$

This expression is in the form \((a + b)^2\), which represents the square of a binomial sum.
The standard algebraic identity for this special product is:

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

Map the terms to the formula

By comparing our expression \((x + 2)^2\) to the general formula \((a + b)^2\), we identify:

• \(a = x\)
• \(b = 2\)

Substitute and simplify each term

Now, we substitute these values into the expanded formula \(a^2 + 2ab + b^2\):

• First term (\(a^2\)):

$$(x)^2 = x^2$$

• Middle term (\(2ab\)):

$$2 \cdot (x) \cdot (2) = 4x$$

• Last term (\(b^2\)):

$$(2)^2 = 4$$

Combine the simplified terms

Combining all three parts gives the final expanded polynomial:

$$x^2 + 4x + 4$$

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).

\((x + 2)^2 =\) <blank>\(x^2 + 4x + 4\)</blank>