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)

Answer 1

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: $$(7-0.5)(7+0.5)$$