Use the polynomial identity of the difference of two squares to write a product equal to 81−16

.(1 point)

1 answer

The polynomial identity for the difference of two squares states that \( a^2 - b^2 = (a - b)(a + b) \).

In your case, you want to express \( 81 - 16 \) using this identity.

First, we recognize that:

  • \( 81 \) can be written as \( 9^2 \) (since \( 9 \times 9 = 81 \)),
  • \( 16 \) can be written as \( 4^2 \) (since \( 4 \times 4 = 16 \)).

Now you can apply the difference of squares identity:

\[ 81 - 16 = 9^2 - 4^2 = (9 - 4)(9 + 4). \]

Calculating the expressions in parentheses, we get:

\[ (9 - 4)(9 + 4) = 5 \cdot 13. \]

Thus, the product equal to \( 81 - 16 \) is:

\[ (9 - 4)(9 + 4) = 5 \cdot 13. \]