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Answer
\( (2t - 1)(2t + 1) = 4t² - 1 \)
Solution
To simplify (2t – 1)(2t + 1), notice that it has the form (a – b)(a + b), which equals a² – b².
Here, a = 2t and b = 1. Therefore, we have:
(2t – 1)(2t + 1) = (2t)² – 1² = 4t² – 1.
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Simplify this solution Extra Insights
Did you know that the expression \( (2t-1)(2t+1) \) represents a special algebraic product known as the difference of squares? When you expand it, you get \( 4t^2 - 1 \). This beautiful identity is a powerful tool in algebra, showing how two binomials can simplify a quadratic expression! When working with expressions like \( (2t-1)(2t+1) \), a common mistake is to forget to apply the distributive property correctly. It’s easy to make errors, like mixing up the signs or accidentally skipping a term. Always double-check your work: you might even find a hidden gem or an unexpected simplification!
