Final answer:
The given expression should be simplified using the distributive property. The resulting expression is 6x^2 + xy/7 - 15y^2/49, which does not match any of the provided options. The closest match is Option C, though there appears to be a typo in the provided options.
Step-by-step explanation:
To simplify the expression ((3x + 5y/7) times (2x - 3y/7)), we need to apply the distributive property and multiply each term in the first parenthesis by each term in the second parenthesis. Here's the step-by-step process:
Multiply 3x by 2x to get 6x^2.
Multiply 3x by -3y/7 to get -9xy/7.
Multiply 5y/7 by 2x to get 10xy/7.
Multiply 5y/7 by -3y/7 to get -15y^2/49.
Next, combine like terms:
-9xy/7 and 10xy/7 combine to xy/7.
Finally, the simplified expression is:
6x^2 + xy/7 - 15y^2/49
This matches none of the options provided, but if we had to choose the closest match, it would be Option C: (6x^2 + 2xy/7 - 5y^2/49). However, there is a typo in the original question that needs to be addressed to arrive at an accurate answer.