Question

3x^2+2y^2 + -×^2-4y^2​

Answer 1

Input Expression

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

Calculates result

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

Solving equation for x

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

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

$\bf \frac{d}{d[y ] } \bigg[ {3x}^{2} + {2y}^{2} + { - x}^{2} - {4y}^{2} \bigg] = - 4y$