Question

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

\\(7x + 1)(7x - 1)\\

Explanation:

Identify the special product pattern

Using the Special Products knowledge point

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

Define the terms for substitution

Identify the terms in the given expression:

$$
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$$

Apply the difference of squares formula

Substitute the terms into the algebraic identity:

$$ (7x+1)(7x-1) = (7x)^2 - (1)^2 $$

Simplify the squared terms

Evaluate each squared term to find the final polynomial:

$$ (7x)^2 - (1)^2 = 49x^2 - 1 $$

Answer:

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

$$(7x + 1)(7x - 1)$$

<blank>\(49x^2 - 1\)</blank>