(4x-3)(x-2)^2=4x^3-19x^2+4x-12

2 min read Jun 16, 2024
(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

  1. Expand (x - 2)²: (x - 2)² = (x - 2)(x - 2) = x² - 2x - 2x + 4 = x² - 4x + 4

  2. Multiply (4x - 3) by the result: (4x - 3)(x² - 4x + 4) = 4x³ - 16x² + 16x - 3x² + 12x - 12

  3. 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.

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