Solve {l}{9x^4-3x^2y^2}{-2y^4}

$$\left. \begin{array} { l } { 9 x ^ { 4 } - 3 x ^ { 2 } y ^ { 2 } } \\ { - 2 y ^ { 4 } } \end{array} \right.$$

Factor

$$\left(3x^{2}-2y^{2}\right)\left(3x^{2}+y^{2}\right)$$

Solution Steps

Consider 9x^{4}-3x^{2}y^{2}-2y^{4} as a polynomial over variable x.

$$9x^{4}-3y^{2}x^{2}-2y^{4}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 9x^{4} and n divides the constant factor -2y^{4}. One such factor is 3x^{2}-2y^{2}. Factor the polynomial by dividing it by this factor.

$$\left(3x^{2}-2y^{2}\right)\left(3x^{2}+y^{2}\right)$$

Evaluate

$$9x^{4}-2y^{4}-3\left(xy\right)^{2}$$