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

1 answer

The difference of two squares can be expressed using the identity:

\[ a^2 - b^2 = (a - b)(a + b) \]

In your case, we want to express \(81 - 16\) using this identity. We can observe that:

\[ 81 = 9^2 \quad \text{and} \quad 16 = 4^2 \]

Thus, we can rewrite \(81 - 16\) as:

\[ 9^2 - 4^2 \]

Applying the difference of squares identity:

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

Calculating the terms:

\[ 9 - 4 = 5 \quad \text{and} \quad 9 + 4 = 13 \]

So, we have:

\[ 81 - 16 = (9 - 4)(9 + 4) = 5 \cdot 13 \]

Therefore, the product equal to \(81 - 16\) is \(5 \cdot 13\).