(x-2)%5E2%3D4x%5E3-19x%5E2%2B4x-12.jpeg "(4x-3)(x-2)^2=4x^3-19x^2+4x-12")
Expanding and Simplifying the Equation: (4x - 3)(x - 2)² = 4x³ - 19x² + 4x - 12
This equation presents a challenge in the form of a product of expressions, one of which is squared. To verify the equation's truth, we'll need to expand both sides and simplify them.
Expanding the Left Side
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Expand (x - 2)²: (x - 2)² = (x - 2)(x - 2) = x² - 2x - 2x + 4 = x² - 4x + 4
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Multiply (4x - 3) by the result: (4x - 3)(x² - 4x + 4) = 4x³ - 16x² + 16x - 3x² + 12x - 12
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Combine like terms: 4x³ - 19x² + 28x - 12
Expanding the Right Side
The right side of the equation is already in its simplest form: 4x³ - 19x² + 4x - 12
Comparing the Results
After simplifying both sides, we see that they are not equal. The left side simplifies to 4x³ - 19x² + 28x - 12, while the right side remains as 4x³ - 19x² + 4x - 12.
Therefore, the given equation (4x - 3)(x - 2)² = 4x³ - 19x² + 4x - 12 is not true.
It's important to note: The equation might be true if there was an error in the provided equation or the intended simplification. Double-checking the original problem statement is crucial.