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: \[ (7 - 0.5)(7 + 0.5) \]