Which of these are the same? 2 (4x²)² - 4x², -(4x)4, (-4x²), 4x4
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Which of these are the same? 2 (4x²)² - 4x², -(4x)4, (-4x²), 4x4
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To determine which of the given expressions are the same, let's simplify each expression step-by-step and compare them:
Expression 1: 2(4x²)² - 4x²
First, we solve the innermost parentheses by squaring 4x²:
2(16x^4) - 4x²
Next, distribute 2 to each term inside the parentheses:
32x^4 - 4x²
Expression 2: -(4x)^4
The expression inside the parentheses can be simplified first:
-(4x)^4 = -(4^4)x^4 = -256x^4
Expression 3: (-4x²)
This expression is already simplified and cannot be combined further.
Expression 4: 4x^4
This expression is already fully simplified.
Now, let's compare the expressions:
Expression 1: 32x^4 - 4x²
Expression 2: -256x^4
Expression 3: (-4x²)
Expression 4: 4x^4
Comparing expression 1 and 2, we can see that they are not the same because they have different coefficients (-256 vs. 32) and exponents (x^4 vs. x^2). So, expressions 1 and 2 are not the same.
Comparing expression 1 and 3, they are also not the same because expression 3 does not contain the exponent x^4 and it has a negative sign (-4x² vs. 32x^4 - 4x²). So, expressions 1 and 3 are not the same.
Comparing expression 1 and 4, we can see that they are not the same because expression 4 does not contain the term -4x². So, expressions 1 and 4 are not the same.
Lastly, comparing expression 2 and 3, we can see that they are not the same either because expression 2 has a different coefficient (-256) and expression 3 has a negative sign. So, expressions 2 and 3 are not the same.
Therefore, none of the given expressions are the same.
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