Solve -32x^4+48x^2y-18y^2=

$$- 32 x ^ { 4 } + 48 x ^ { 2 } y - 18 y ^ { 2 } =$$

Factor

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

Solution Steps

Factor out 2.

$$2\left(-16x^{4}+24x^{2}y-9y^{2}\right)$$

Consider -16x^{4}+24x^{2}y-9y^{2}. Consider -16x^{4}+24x^{2}y-9y^{2} as a polynomial over variable x.

$$-16x^{4}+24yx^{2}-9y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -16x^{4} and n divides the constant factor -9y^{2}. One such factor is 4x^{2}-3y. Factor the polynomial by dividing it by this factor.

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

Rewrite the complete factored expression.

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

Evaluate

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