(5-x)((2-x)(5-x)-4)+2(-2(5-x)+8)+4(-4+4(2-x))

asked by guest
on Nov 14, 2024 at 2:53 pm



You asked:

Evaluate the expression: \(\left(5 - x\right) \cdot \left(\left(2 - x\right) \cdot \left(5 - x\right) - 4\right) + 2 \cdot \left(-\left( 2 \cdot \left(5 - x\right) \right) + 8\right) + 4 \cdot \left(-4 + 4 \cdot \left(2 - x\right)\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(5 - x\right) \cdot \left(\left(2 - x\right) \cdot \left(5 - x\right) - 4\right) + 2 \cdot \left(-\left( 2 \cdot \left(5 - x\right) \right) + 8\right) + 4 \cdot \left(-4 + 4 \cdot \left(2 - x\right)\right) = - 12 x + \left(5 - x\right) \left(\left(2 - x\right) \left(5 - x\right) - 4\right) + 12 \)

Expanded

\[\left(5 - x\right) \cdot \left(\left(2 - x\right) \cdot \left(5 - x\right) - 4\right) + 2 \cdot \left(-\left( 2 \cdot \left(5 - x\right) \right) + 8\right) + 4 \cdot \left(-4 + 4 \cdot \left(2 - x\right)\right) = - x^{3} + 12 x^{2} - 53 x + 42\]

Factored

\[\left(5 - x\right) \cdot \left(\left(2 - x\right) \cdot \left(5 - x\right) - 4\right) + 2 \cdot \left(-\left( 2 \cdot \left(5 - x\right) \right) + 8\right) + 4 \cdot \left(-4 + 4 \cdot \left(2 - x\right)\right) = - \left(x - 1\right) \left(x^{2} - 11 x + 42\right)\]

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