(-3x³y⁴ + 12xyz² - 5)(15 - 2x²y - 2xy)

asked by guest
on Feb 01, 2025 at 10:26 am



You asked:

Evaluate the expression: (−(3x3y4)+12xyz2−5)(15−2x2y−2xy)\left(-\left( 3 {x}^{3} {y}^{4} \right) + 12 x y {z}^{2} - 5\right) \left(15 - 2 {x}^{2} y - 2 x y\right)

MathBot Answer:

Evaluated



(−(3x3y4)+12xyz2−5)(15−2x2y−2xy)=(−2x2y−2xy+15)(−3x3y4+12z2xy−5)\displaystyle \left(-\left( 3 {x}^{3} {y}^{4} \right) + 12 x y {z}^{2} - 5\right) \left(15 - 2 {x}^{2} y - 2 x y\right) = \left(- 2 x^{2} y - 2 x y + 15\right) \left(- 3 x^{3} y^{4} + 12 z^{2} x y - 5\right)

Expanded

(−(3x3y4)+12xyz2−5)(15−2x2y−2xy)=6x5y5+6x4y5−45x3y4−24x3y2z2−24x2y2z2+10x2y+180z2xy+10xy−75\left(-\left( 3 {x}^{3} {y}^{4} \right) + 12 x y {z}^{2} - 5\right) \left(15 - 2 {x}^{2} y - 2 x y\right) = 6 x^{5} y^{5} + 6 x^{4} y^{5} - 45 x^{3} y^{4} - 24 x^{3} y^{2} z^{2} - 24 x^{2} y^{2} z^{2} + 10 x^{2} y + 180 z^{2} x y + 10 x y - 75

Factored

(−(3x3y4)+12xyz2−5)(15−2x2y−2xy)=(2x2y+2xy−15)(3x3y4−12z2xy+5)\left(-\left( 3 {x}^{3} {y}^{4} \right) + 12 x y {z}^{2} - 5\right) \left(15 - 2 {x}^{2} y - 2 x y\right) = \left(2 x^{2} y + 2 x y - 15\right) \left(3 x^{3} y^{4} - 12 z^{2} x y + 5\right)

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