Solve 12x^4+32x^2y^3+21y^6

$$12 x ^ { 4 } + 32 x ^ { 2 } y ^ { 3 } + 21 y ^ { 6 }$$

Factor

$$\left(2x^{2}+3y^{3}\right)\left(6x^{2}+7y^{3}\right)$$

Solution Steps

Consider 12x^{4}+32x^{2}y^{3}+21y^{6} as a polynomial over variable x.

$$12x^{4}+32y^{3}x^{2}+21y^{6}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power 12x^{4} and n divides the constant factor 21y^{6}. One such factor is 2x^{2}+3y^{3}. Factor the polynomial by dividing it by this factor.

$$\left(2x^{2}+3y^{3}\right)\left(6x^{2}+7y^{3}\right)$$

Evaluate

$$12x^{4}+32x^{2}y^{3}+21y^{6}$$