Question
Write the product of 6.5 and 7.5 using the difference of two squares identity. * 2 points (7 + 0.5)(7 - 0.5) (6.5 + 0.5)(7.5 - 0.5) (7 + 0.5)(6 - 0.5) (6.5 - 0.5)(7.5 + 0.5)
Answers
GPT-4o mini
To calculate the product of 6.5 and 7.5 using the difference of two squares identity, we can express the numbers in a way that fits the formula:
The difference of two squares identity states that \( a^2 - b^2 = (a + b)(a - b) \).
We can rewrite \( 6.5 \) and \( 7.5 \) in terms of their average and half the difference:
\[
6.5 = 7 - 0.5
\]
\[
7.5 = 7 + 0.5
\]
Using the difference of two squares identity:
\[
6.5 \times 7.5 = (7 - 0.5)(7 + 0.5)
\]
Now substituting into the identity:
\[
(7 - 0.5)(7 + 0.5) = 7^2 - (0.5)^2
\]
Calculating this gives:
\[
7^2 - (0.5)^2 = 49 - 0.25 = 48.75
\]
Thus, the product of \( 6.5 \) and \( 7.5 \) using the difference of two squares identity is:
\[
6.5 \times 7.5 = 48.75
\]
Among the options provided, the expression that corresponds to our derivation is:
\[
(7 - 0.5)(7 + 0.5)
\]
So your answer is:
\[
(7 - 0.5)(7 + 0.5)
\]
The difference of two squares identity states that \( a^2 - b^2 = (a + b)(a - b) \).
We can rewrite \( 6.5 \) and \( 7.5 \) in terms of their average and half the difference:
\[
6.5 = 7 - 0.5
\]
\[
7.5 = 7 + 0.5
\]
Using the difference of two squares identity:
\[
6.5 \times 7.5 = (7 - 0.5)(7 + 0.5)
\]
Now substituting into the identity:
\[
(7 - 0.5)(7 + 0.5) = 7^2 - (0.5)^2
\]
Calculating this gives:
\[
7^2 - (0.5)^2 = 49 - 0.25 = 48.75
\]
Thus, the product of \( 6.5 \) and \( 7.5 \) using the difference of two squares identity is:
\[
6.5 \times 7.5 = 48.75
\]
Among the options provided, the expression that corresponds to our derivation is:
\[
(7 - 0.5)(7 + 0.5)
\]
So your answer is:
\[
(7 - 0.5)(7 + 0.5)
\]