QuestionAugust 27, 2025

Which expression is equivalent to 100n^2-1 7 (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 7 (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 7
(10n)^2-(1)^2
(10n^2)^2-(1)^2
(50n)^2-(1)^2
(50n^2)^2-(1)^2

Solution
4.5(233 votes)

Answer

(10n)^{2}-(1)^{2} Explanation 1. Recognize the form The expression 100n^2 - 1 is a difference of squares: a^2 - b^2. 2. Identify a and b Compare with (an)^2 - (b)^2: Here, a = 10n and b = 1. 3. Verify equivalence Substitute a = 10n and b = 1 into (a)^2 - (b)^2: (10n)^2 - (1)^2 = 100n^2 - 1.

Explanation

1. Recognize the form<br /> The expression $100n^2 - 1$ is a difference of squares: $a^2 - b^2$.<br /><br />2. Identify $a$ and $b$<br /> Compare with $(an)^2 - (b)^2$: Here, $a = 10n$ and $b = 1$.<br /><br />3. Verify equivalence<br /> Substitute $a = 10n$ and $b = 1$ into $(a)^2 - (b)^2$: $(10n)^2 - (1)^2 = 100n^2 - 1$.
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