220-10w^2 ((270-13w^2)(350-15w^2)-(-150)(150))-(-120)((-120)(350-15w^2)-(0)(150))

asked by guest
on Nov 25, 2024 at 7:44 am



You asked:

Evaluate the expression: \(220 - 10 {w}^{2} \cdot \left(\left(270 - 13 {w}^{2}\right) \cdot \left(350 - 15 {w}^{2}\right) - -150 \cdot 150\right) - -120 \cdot \left(-120 \cdot \left(350 - 15 {w}^{2}\right) - 0 \cdot 150\right)\)

MathBot Answer:

Evaluated



\(\displaystyle 220 - 10 {w}^{2} \cdot \left(\left(270 - 13 {w}^{2}\right) \cdot \left(350 - 15 {w}^{2}\right) - -150 \cdot 150\right) - -120 \cdot \left(-120 \cdot \left(350 - 15 {w}^{2}\right) - 0 \cdot 150\right) = - 10 w^{2} \left(\left(270 - 13 w^{2}\right) \left(350 - 15 w^{2}\right) + 22500\right) + 216000 w^{2} - 5039780 \)

Expanded

\[220 - 10 {w}^{2} \cdot \left(\left(270 - 13 {w}^{2}\right) \cdot \left(350 - 15 {w}^{2}\right) - -150 \cdot 150\right) - -120 \cdot \left(-120 \cdot \left(350 - 15 {w}^{2}\right) - 0 \cdot 150\right) = - 1950 w^{6} + 86000 w^{4} - 954000 w^{2} - 5039780\]

Factored

\[220 - 10 {w}^{2} \cdot \left(\left(270 - 13 {w}^{2}\right) \cdot \left(350 - 15 {w}^{2}\right) - -150 \cdot 150\right) - -120 \cdot \left(-120 \cdot \left(350 - 15 {w}^{2}\right) - 0 \cdot 150\right) = - 10 \cdot \left(195 w^{6} - 8600 w^{4} + 95400 w^{2} + 503978\right)\]

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