Solve 1/27-b^6y^6

$$\frac { 1 } { 27 } - b ^ { 6 } y ^ { 6 }$$

Factor

$$\frac{\left(3b^{2}y^{2}-1\right)\left(-9b^{4}y^{4}-3b^{2}y^{2}-1\right)}{27}$$

Solution Steps

Factor out \frac{1}{27}.

$$\frac{1-27b^{6}y^{6}}{27}$$

Consider 1-27b^{6}y^{6}. Consider 1-27b^{6}y^{6} as a polynomial over variable b.

$$-27y^{6}b^{6}+1$$

Find one factor of the form ky^{m}b^{n}+p, where ky^{m}b^{n} divides the monomial with the highest power -27y^{6}b^{6} and p divides the constant factor 1. One such factor is 3b^{2}y^{2}-1. Factor the polynomial by dividing it by this factor.

$$\left(3b^{2}y^{2}-1\right)\left(-9b^{4}y^{4}-3b^{2}y^{2}-1\right)$$

Rewrite the complete factored expression.

$$\frac{\left(3b^{2}y^{2}-1\right)\left(-9b^{4}y^{4}-3b^{2}y^{2}-1\right)}{27}$$

Evaluate

$$\frac{1}{27}-\left(by\right)^{6}$$