Question
Multiply and simplify completely: \( (4 x-2)^{2} \)
Ask by Gray Henry. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(16x^2 - 16x + 4\)
Solution
Calculate or simplify the expression \( (4x-2)^2 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(4x-2\right)^{2}\)
- step1: Calculate:
\(16x^{2}-16x+4\)
The simplified form of \((4x-2)^2\) is \(16x^2 - 16x + 4\).
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Simplify this solution The Deep Dive
To simplify \( (4x - 2)^{2} \), we can use the formula for squaring a binomial, which is \( (a - b)^{2} = a^{2} - 2ab + b^{2} \). Here, \( a = 4x \) and \( b = 2 \). Calculating each term, we have: 1. \( (4x)^{2} = 16x^{2} \) 2. \( -2(4x)(2) = -16x \) 3. \( (2)^{2} = 4 \) Now put it all together: \[ (4x - 2)^{2} = 16x^{2} - 16x + 4 \] So, the simplified expression is \( 16x^{2} - 16x + 4 \).
