Question
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Answer
\( (2 \sqrt{5}-7)^{2} = 69 - 28\sqrt{5} \)
Solution
Calculate or simplify the expression \( (2 \sqrt{5}-7)^{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(\left(2\sqrt{5}-7\right)^{2}\)
- step1: Expand the expression:
\(\left(2\sqrt{5}\right)^{2}-2\times 2\sqrt{5}\times 7+7^{2}\)
- step2: Calculate:
\(20-28\sqrt{5}+49\)
- step3: Add the numbers:
\(69-28\sqrt{5}\)
The simplified form of \( (2 \sqrt{5}-7)^{2} \) is \( 69-28\sqrt{5} \).
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Simplify this solution Bonus Knowledge
To expand \( (2 \sqrt{5}-7)^{2} \), you can use the square of a binomial formula, \( (a - b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = 2 \sqrt{5} \) and \( b = 7 \). Calculating each term: 1. \( (2 \sqrt{5})^{2} = 4 \times 5 = 20 \) 2. \( -2 \times (2 \sqrt{5}) \times 7 = -28 \sqrt{5} \) 3. \( 7^{2} = 49 \) Putting it all together: \( (2 \sqrt{5}-7)^{2} = 20 - 28 \sqrt{5} + 49 = 69 - 28 \sqrt{5} \). So the final answer is: \( 69 - 28 \sqrt{5} \).
