Question
b) \( \left(x^{2}-2 x\right)^{2}+2 x^{2}-4 x+1 \)
Ask by Sherman Rose. in Serbia
Nov 04,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x^{4}-4x^{3}+6x^{2}-4x+1 \)
Solution
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The Deep Dive
To tackle the expression \( \left(x^{2}-2 x\right)^{2}+2 x^{2}-4 x+1 \), we can start by simplifying it step-by-step. First, let's expand \( (x^2 - 2x)^2 \): \[ (x^2 - 2x)^2 = x^4 - 4x^3 + 4x^2 \] Now, we can substitute this back into the expression: \[ x^4 - 4x^3 + 4x^2 + 2x^2 - 4x + 1 \] Combine like terms: \[ x^4 - 4x^3 + (4x^2 + 2x^2) - 4x + 1 = x^4 - 4x^3 + 6x^2 - 4x + 1 \] So the simplified form of \( \left(x^{2}-2 x\right)^{2}+2 x^{2}-4 x+1 \) is: \[ x^4 - 4x^3 + 6x^2 - 4x + 1 \]
