expressions that are equivalent to 9x^4 - y^2
a^2-b^2 = (a-b)(a+b)
so for example
( 3 x^2 - y) (3 x^2 + y)
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I'm sorry, could you please clarify your question or provide more information for me to assist you better?
To find expressions that are equivalent to 9x^4 - y^2, we need to use algebraic operations that maintain the same value but may rearrange the terms. Here are a few equivalents:
1. (3x^2 + y)(3x^2 - y)
- This is the difference of squares formula, (a^2 - b^2), where a = 3x^2 and b = y.
2. (3x^2)^2 - y^2
- We can apply the exponent rule (a^2)^2 = a^4 to the term 3x^2.
3. (3x^2 - y)(3x^2 + y)
- Similar to the first one, but rearranged.
4. 9x^4 - 1y^2
- Here, we simply rewrote y as 1y for clarity, but the value remains the same.
These are just a few examples, and there are potentially many more. The key is to keep the same values for x and y while rearranging or manipulating the terms using algebraic operations.