Question
Simplify the following expression: \[ (2 x+8)(2 x-8)+(2-5 x)^{2} \] \( 29 x^{2}-52 x-60 \) \( 29 x^{2}-20 x-60 \) \( 29 x^{2}+20 x-60 \) \( 29 x^{2}+52 x-60 \)
Ask by Harris Chang. in Canada
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \(29x^{2}-20x-60\).
Solution
Calculate or simplify the expression \( (2x+8)(2x-8)+(2-5x)^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(2x+8\right)\left(2x-8\right)+\left(2-5x\right)^{2}\)
- step1: Expand the expression:
\(4x^{2}-64+\left(2-5x\right)^{2}\)
- step2: Expand the expression:
\(4x^{2}-64+4-20x+25x^{2}\)
- step3: Add the terms:
\(29x^{2}-60-20x\)
The simplified expression is \(29x^{2}-60-20x\).
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Simplify this solution Bonus Knowledge
To simplify the expression \((2 x+8)(2 x-8)+(2-5 x)^{2}\), let's break it down step by step. First, we can apply the difference of squares to the first part: \[ (2x + 8)(2x - 8) = (2x)^2 - (8)^2 = 4x^2 - 64 \] Now, let's expand the second part: \[ (2 - 5x)^2 = 2^2 - 2 \cdot 2 \cdot 5x + (5x)^2 = 4 - 20x + 25x^2 \] Now, combine both results: \[ 4x^2 - 64 + (4 - 20x + 25x^2) \] Combine like terms: \[ (4x^2 + 25x^2) + (-20x) + (4 - 64) = 29x^2 - 20x - 60 \] The simplified expression is: \[ 29x^2 - 20x - 60 \] So the correct answer is: \(\boxed{29 x^{2}-20 x-60}\)
