(1-x)(-x^3)+(1-x)^3(3x)-(1-x)^4

asked by guest
on Apr 06, 2025 at 8:53 pm



You asked:

Evaluate the expression: (1−x)⋅−x3+(1−x)3⋅3x−(1−x)4\left(1 - x\right) \cdot -{x}^{3} + {\left( 1 - x \right)}^{3} \cdot 3 x - {\left( 1 - x \right)}^{4}

MathBot Answer:

Evaluated



(1−x)⋅−x3+(1−x)3⋅3x−(1−x)4=−x3⋅(1−x)+3x(1−x)3−(1−x)4\displaystyle \left(1 - x\right) \cdot -{x}^{3} + {\left( 1 - x \right)}^{3} \cdot 3 x - {\left( 1 - x \right)}^{4} = - x^{3} \cdot \left(1 - x\right) + 3 x \left(1 - x\right)^{3} - \left(1 - x\right)^{4}

Expanded

(1−x)⋅−x3+(1−x)3⋅3x−(1−x)4=−3x4+12x3−15x2+7x−1\left(1 - x\right) \cdot -{x}^{3} + {\left( 1 - x \right)}^{3} \cdot 3 x - {\left( 1 - x \right)}^{4} = - 3 x^{4} + 12 x^{3} - 15 x^{2} + 7 x - 1

Factored

(1−x)⋅−x3+(1−x)3⋅3x−(1−x)4=−(x−1)(3x3−9x2+6x−1)\left(1 - x\right) \cdot -{x}^{3} + {\left( 1 - x \right)}^{3} \cdot 3 x - {\left( 1 - x \right)}^{4} = - \left(x - 1\right) \left(3 x^{3} - 9 x^{2} + 6 x - 1\right)

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