\(=\left(x-2\right)^2+2\left(x-2\right)\left(2x+2\right)+\left(2x+2\right)^2\)

\(=\left(x-2+2x+2\right)^2=\left(3x\right)^2=9x^2\)

A = (x - 1)³ - x(x - 2)² + 1

A = (x - 1)(x² - 2x + 1) - x(x - 2)² + 1

A = x(x² - 2x + 1) - (x² - 2x + 1) - x(x - 2)² + 1

A = x³ - 2x² + x - (x² - 2x + 1) - x(x² - 2x.2 + 2²) + 1

A = x³ - 2x² + x - (x² - 2x + 1) - (x³ - 4x² + 4x) + 1

A = x³ - 2x² + x - x² + 2x - 1 - x³ + 4x² - 4x + 1

A = (x³ - x³) + (-2x² - x² + 4x²) + (x + 2x - 4x) + (-1 + 1)

A = x² - x

B = (-x - 2)³ + (2x - 4)(x² + 2x + 4) - x²(x - 6)

B = (-x - 2)[(-x²) - 2.(-x).2 + 2²] + (2x - 4)(x² + 2x + 4) - x²(x - 6)

B = -x[(-x)² - 2.(-x).2 + 2²] - 2[(-x)² - 2.(-x).2 + 2²] + (2x - 4)(x² + 2x + 4) - x²(x - 6)

B = -(x³ + 4x² + 4x) - (2x² + 4x + 8) + 2x(x² + 2x + 4) - 4(x² + 2x + 4) - x²(x - 6)

B = -(x³ + 4x² - 4x) - (2x² + 4x + 8) + 2x³ + 4x² + 8x - (x² + 8x + 16) - (x³ - 6x²)

B = -x³ - 4x² + 4x - 2x² - 4x - 8 + 2x³ + 4x² + 8x - x² - 8x - 16 - x³ + 6x²

B = (-x³ + 2x³ - x³) + (-4x² - 2x² + 4x² - x² + 6x²) + (-4x - 8x + 8x - 8x) + (-8 - 16)

B = -12x - 24

a: =18x^3y^2-12x^3y^3+6x^2y^2

b: (-3x+2)(5x^2-1/3x+4)

=-12x^3+x^2-12x+10x^2-2/3x+8

=-12x^3+11x^2-38/3x+8

c: =x^2-x-2+3x-x^2

=2x-2

d: =4x^2+12x+9-4x^2+25-(x-1)(x^2+12)

=12x+34-x^3-12x+x^2+12

=-x^3+x^2+46

\(P\left(x\right)=2x^4+3x^2-x^3-3x^4-x^2-2x+1\)

\(=-x^4-x^3+2x^2-2x+1\)

C

F(\(x\)) = -2\(x\)⁴ + 3\(x^3\) - 4\(x\) + 2\(x^4\) - \(x^2\) - 3\(x^3\) - \(x\) + 1

F(\(x\)) = ( -2\(x^4\)+2\(x^4\)) + (3\(x^3\) - 3\(x^3\)) -(4\(x\) + \(x\)) + 1

F(\(x\)) = 0 + 0 - 5\(x\) + 1

F(\(x\)) = - 5\(x\) + 1

\(f\left(x\right)=-2x^4+3x^3-4x+2x^4-x^2-3x^3-x+1\)

\(f\left(x\right)=-2x^4+2x^4+3x^3-3x^3-4x-x-x^2+1\)

\(f\left(x\right)=-5x-x^2+1\)

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