2(x squared plus 3/2 y squared) multiplied by -2/3 multiplied by (6x squared minus 3y squared plus 5)

asked by guest
on Nov 18, 2024 at 10:26 pm



You asked:

Evaluate the expression: \(2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3} \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right)\)

MathBot Answer:

Evaluated



\(\displaystyle 2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3} \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right) = - \frac{4 \left(x^{2} + \frac{3 y^{2}}{2}\right) \left(6 x^{2} - 3 y^{2} + 5\right)}{3} \)

Expanded

\[2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3} \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right) = - 8 x^{4} - 8 x^{2} y^{2} - \frac{20 x^{2}}{3} + 6 y^{4} - 10 y^{2}\]

Factored

\[2 \cdot \left({x}^{2} + \frac{3}{2} \cdot {y}^{2}\right) \cdot \frac{-2}{3} \cdot \left(6 \cdot {x}^{2} - 3 \cdot {y}^{2} + 5\right) = - \frac{2 \cdot \left(2 x^{2} + 3 y^{2}\right) \left(6 x^{2} - 3 y^{2} + 5\right)}{3}\]

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