Question

Find the product of (x + 7)(x − 7).

Answer 1

Whenever a question asks you to multiply binomials, just remember FOIL.
Multiply FIRST terms with FIRST terms
Multiply OUTER terms with OUTER terms
Multiply INNER terms with INNER terms
Multiply LAST terms with LAST terms

first x first = (x)(x) = $x^{2}$
outer x outer = (x)(-7) = -7x
inner x inner = (7)(x) = 7x
last x last = (7)(-7) = -49
Now add all of the products up to get your final answer.
$x^{2}$ - 7x + 7x - 49 = $x^{2}$ - 49

Answer 2

$(a+b)(a-b)=a^2-b^2\\ \Downarrow\\ (x + 7)(x - 7)=x^2-49$