Question
The expression (3x - 4y3)(3x + 4y?) is equivalent to:
A. 9x2-1614
B. 9x - 8y*
C. 9x7 + 164*
D. 6x2 - 16รท*
E. 6x7 - 8y*
A. 9x2-1614
B. 9x - 8y*
C. 9x7 + 164*
D. 6x2 - 16รท*
E. 6x7 - 8y*
Answers
GPT-4o mini
To simplify the expression \((3x - 4y^3)(3x + 4y^3)\), we can utilize the difference of squares formula, which states that \((a - b)(a + b) = a^2 - b^2\).
Here, we can identify:
- \(a = 3x\)
- \(b = 4y^3\)
Now applying the difference of squares formula:
\[
(3x - 4y^3)(3x + 4y^3) = (3x)^2 - (4y^3)^2
\]
Calculating each square:
\[
(3x)^2 = 9x^2
\]
\[
(4y^3)^2 = 16y^6
\]
Putting it all together, we have:
\[
9x^2 - 16y^6
\]
None of the answer choices seem to match this expression exactly, but we see that:
**The correct simplification is:**
\[
9x^2 - 16y^6
\]
Given that no answer choices appear to match this calculation directly, it may be worthwhile to verify if the question or options contain typographical errors. If "16" or "y" were to be slightly different, that might lead to a match with an option, but currently, the simplified form is correct as derived.
Here, we can identify:
- \(a = 3x\)
- \(b = 4y^3\)
Now applying the difference of squares formula:
\[
(3x - 4y^3)(3x + 4y^3) = (3x)^2 - (4y^3)^2
\]
Calculating each square:
\[
(3x)^2 = 9x^2
\]
\[
(4y^3)^2 = 16y^6
\]
Putting it all together, we have:
\[
9x^2 - 16y^6
\]
None of the answer choices seem to match this expression exactly, but we see that:
**The correct simplification is:**
\[
9x^2 - 16y^6
\]
Given that no answer choices appear to match this calculation directly, it may be worthwhile to verify if the question or options contain typographical errors. If "16" or "y" were to be slightly different, that might lead to a match with an option, but currently, the simplified form is correct as derived.