(27$x^{2}$ + 18x - 1)(3 $x^{3}$ - $x^{2}$ -3x +1)(3x-1)

asked by guest
on Oct 25, 2024 at 10:27 am



You asked:

Evaluate the expression: \(\left(27 \cdot {x}^{2} + 18 x - 1\right) \cdot \left(3 \cdot {x}^{3} - {x}^{2} - 3 x + 1\right) \cdot \left(3 x - 1\right)\)

MathBot Answer:

Evaluated



\(\displaystyle \left(27 \cdot {x}^{2} + 18 x - 1\right) \cdot \left(3 \cdot {x}^{3} - {x}^{2} - 3 x + 1\right) \cdot \left(3 x - 1\right) = \left(3 x - 1\right) \left(27 x^{2} + 18 x - 1\right) \left(3 x^{3} - x^{2} - 3 x + 1\right) \)

Expanded

\[\left(27 \cdot {x}^{2} + 18 x - 1\right) \cdot \left(3 \cdot {x}^{3} - {x}^{2} - 3 x + 1\right) \cdot \left(3 x - 1\right) = 243 x^{6} - 333 x^{4} + 24 x^{3} + 89 x^{2} - 24 x + 1\]

Factored

\[\left(27 \cdot {x}^{2} + 18 x - 1\right) \cdot \left(3 \cdot {x}^{3} - {x}^{2} - 3 x + 1\right) \cdot \left(3 x - 1\right) = \left(3 x - 1\right)^{2} \left(x - 1\right) \left(x + 1\right) \left(27 x^{2} + 18 x - 1\right)\]

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