QuestionAugust 27, 2025

Which expression is equivalent to 100n^2-1 (10n)^2-(1)^2 (10n^2)^2-(1)^2 (50n)^2-(1)^2 (50n^2)^2-(1)^2

Which expression is equivalent to 100n^2-1 (10n)^2-(1)^2 (10n^2)^2-(1)^2 (50n)^2-(1)^2 (50n^2)^2-(1)^2
Which expression is equivalent to 100n^2-1
(10n)^2-(1)^2
(10n^2)^2-(1)^2
(50n)^2-(1)^2
(50n^2)^2-(1)^2

Solution
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Answer

(10n)^{2}-(1)^{2} Explanation 1. Identify the form of the expression 100n^2 - 1 is a difference of squares: a^2 - b^2. 2. Apply the difference of squares formula **(a^2 - b^2) = (a - b)(a + b)**. Here, a = 10n and b = 1. 3. Verify equivalent expression (10n)^2 - 1^2 = 100n^2 - 1. This matches the original expression.

Explanation

1. Identify the form of the expression<br /> $100n^2 - 1$ is a difference of squares: $a^2 - b^2$.<br />2. Apply the difference of squares formula<br /> **$(a^2 - b^2) = (a - b)(a + b)$**. Here, $a = 10n$ and $b = 1$.<br />3. Verify equivalent expression<br /> $(10n)^2 - 1^2 = 100n^2 - 1$. This matches the original expression.
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