3x^2+2y^2 + -×^2-4y^2

1.	3x^2+2y^2 + -×^2-4y^2
Answer» Input EXPRESSION $\bf {3x}^{2} + {2y}^{2} + { - x}^{2} - {4y}^{2}$ CALCULATES result $\bf 2x \: (x - y) \: (x + y)$ Solving equation for x $\bf {3x}^{2} + {2y}^{2} + { - x}^{2} + {4y}^{2} = 0 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: \: \: \big[ y = - x \big] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: \: \: \big[ y = x \big]$ Graph simplify $\bf 2 \times ( {x}^{2} - {y}^{2} )$ Expand $\bf {2x}^{2} - {2y}^{2}$ Factor $\bf - 2 \times ( - x + y)( x + y)$ Alternative form $\bf - 2( { - x}^{2} + {y}^{2} )$ Polynomial discrimination with respect to x $\bf \triangle = {16y}^{2}$ PARTIAL derivative with respect to x $\bf \frac{d}{d[ x] } \bigg[ {3x}^{2} + {2y}^{2} + { - x}^{2} - {4y}^{2} \bigg] = 4x$ Partial derivative with respect to Y $\bf \frac{d}{d[y ] } \bigg[ {3x}^{2} + {2y}^{2} + { - x}^{2} - {4y}^{2} \bigg] = - 4y$

Answer»

$\bf {3x}^{2} + {2y}^{2} + { - x}^{2} - {4y}^{2}$

CALCULATES result

$\bf 2x \: (x - y) \: (x + y)$

Solving equation for x

$\bf {3x}^{2} + {2y}^{2} + { - x}^{2} + {4y}^{2} = 0 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: \: \: \big[ y = - x \big] \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \: \: \: \big[ y = x \big]$