To solve [tex]\(81 - 16\)[/tex] using the difference of squares identity, we start by recognizing that both 81 and 16 are perfect squares.
First, we can express each number as a square:
[tex]\[ 81 = 9^2 \][/tex]
[tex]\[ 16 = 4^2 \][/tex]
The polynomial identity for the difference of two squares is given by:
[tex]\[ a^2 - b^2 = (a - b)(a + b) \][/tex]
Identifying [tex]\(a\)[/tex] and [tex]\(b\)[/tex] in this context, we have:
[tex]\[ a = 9 \][/tex]
[tex]\[ b = 4 \][/tex]
Using the difference of squares identity, substitute [tex]\(a\)[/tex] and [tex]\(b\)[/tex] into the formula:
[tex]\[ 9^2 - 4^2 = (9 - 4)(9 + 4) \][/tex]
Calculate the expressions inside the parentheses:
[tex]\[ 9 - 4 = 5 \][/tex]
[tex]\[ 9 + 4 = 13 \][/tex]
Now multiply these results together:
[tex]\[ (9 - 4)(9 + 4) = 5 \cdot 13 = 65 \][/tex]
Hence, the product that equals [tex]\(81 - 16\)[/tex] is:
[tex]\[ \boxed{65} \][/tex]
