(7х²-2х+4-х²) (2х-1)

To simplify the expression \((7x^2 - 2x + 4 - x^2)(2x - 1)\), we first combine like terms in the first part of the expression: 1. Combine \(7x^2\) and \(-x^2\): \[ 7x^2 - x^2 = 6x^2 \] So, the expression simplifies to: \[ (6x^2 - 2x + 4)(2x - 1) \] Now, we can expand this expression using the distributive property (also known as the FOIL method for binomials): \[ (6x^2)(2x) + (6x^2)(-1) + (-2x)(2x) + (-2x)(-1) + (4)(2x) + (4)(-1) \] Calculating each term: 1. \(6x^2 \cdot 2x = 12x^3\) 2. \(6x^2 \cdot (-1) = -6x^2\) 3. \(-2x \cdot 2x = -4x^2\) 4. \(-2x \cdot (-1) = 2x\) 5. \(4 \cdot 2x = 8x\) 6. \(4 \cdot (-1) = -4\) Now, combining all these results: \[ 12x^3 + (-6x^2 - 4x^2) + (2x + 8x) - 4 \] Combine like terms: - For \(x^3\): \(12x^3\) - For \(x^2\): \(-6x^2 - 4x^2 = -10x^2\) - For \(x\): \(2x + 8x = 10x\) So the final result is: \[ 12x^3 - 10x^2 + 10x - 4 \] Thus, the simplified expression is: \[ \boxed{12x^3 - 10x^2 + 10x - 4} \]