3\left(x^2+3x\right)^2\left(2x+3\right)\left(1-2x\right)^{\frac{3}{2}}-3\left(x^2+3x\right)^3\left(1-2x\right)^{\frac{1}{2}}

asked by guest
on Oct 21, 2024 at 12:30 am



You asked:

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

MathBot Answer:

Evaluated



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

Expanded

\[3 \cdot {\left( {x}^{2} + 3 x \right)}^{2} \cdot \left(2 x + 3\right) \cdot {\left( 1 - 2 x \right)}^{\frac{3}{2}} - 3 \cdot {\left( {x}^{2} + 3 x \right)}^{3} \cdot {\left( 1 - 2 x \right)}^{\frac{1}{2}} = - 15 x^{6} \sqrt{1 - 2 x} - 111 x^{5} \sqrt{1 - 2 x} - 252 x^{4} \sqrt{1 - 2 x} - 135 x^{3} \sqrt{1 - 2 x} + 81 x^{2} \sqrt{1 - 2 x}\]

Factored

\[3 \cdot {\left( {x}^{2} + 3 x \right)}^{2} \cdot \left(2 x + 3\right) \cdot {\left( 1 - 2 x \right)}^{\frac{3}{2}} - 3 \cdot {\left( {x}^{2} + 3 x \right)}^{3} \cdot {\left( 1 - 2 x \right)}^{\frac{1}{2}} = - 3 x^{2} \sqrt{1 - 2 x} \left(x + 3\right)^{2} \cdot \left(5 x^{2} + 7 x - 3\right)\]

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