Question

Write the product of 10.5 and 20.5 using the difference of two squares identity.(1 point)
Responses

(15.5 + 5)(15.5 - 5)
(15.5 + 5)(15.5 - 5)

(15.5 - 5)(25.5 - 5)
(15.5 - 5)(25.5 - 5)

(5.5 + 5)(20.5 - 5)
(5.5 + 5)(20.5 - 5)

(15.5 + 5)(5.5 + 5)

Answer 1

To find the product of 10.5 and 20.5 using the difference of two squares identity, we first express both 10.5 and 20.5 in relation to their average.

The average of 10.5 and 20.5 is:

\[
\frac{10.5 + 20.5}{2} = \frac{31}{2} = 15.5
\]

Now, we can express 10.5 and 20.5 as:

\[
10.5 = 15.5 - 5 \quad \text{and} \quad 20.5 = 15.5 + 5
\]

Using the difference of squares identity, which states that \( (a-b)(a+b) = a^2 - b^2 \):

Let \( a = 15.5 \) and \( b = 5 \).

Now we can write the product as:

\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5) = 15.5^2 - 5^2
\]

Among the responses you provided, the correct form of applying the difference of squares is:

\[
(15.5 + 5)(15.5 - 5)
\]

So, the answer is:

**(15.5 + 5)(15.5 - 5)**