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).

\\(4x + 9)^2\\

Explanation:

Identify the appropriate special product

Using the Square of a Binomial Sum knowledge point
The given expression is:

$$ (4x + 9)^2 $$

This matches the binomial sum square form:

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

Assign values to the variables

Using the Square of a Binomial Sum knowledge point
Identify the terms:

$$
LATEXBLOCK0
$$

Expand the squared terms

Using the Square of a Binomial Sum knowledge point
Calculate the individual parts:

$$
LATEXBLOCK1
$$

Calculate the middle term

Using the Square of a Binomial Sum knowledge point
Multiply the terms:

$$ 2ab = 2(4x)(9) = 72x $$

Combine the expanded terms

Using the Square of a Binomial Sum knowledge point
Assemble the final polynomial:

$$ 16x^2 + 72x + 81 $$

Answer:

\(16x^2 + 72x + 81\)