Solve 5a^3b^6-40x^3y^6

$$5 a ^ { 3 } b ^ { 6 } - 40 x ^ { 3 } y ^ { 6 }$$

Factor

$$5\left(ab^{2}-2xy^{2}\right)\left(4x^{2}y^{4}+2axb^{2}y^{2}+a^{2}b^{4}\right)$$

Solution Steps

Factor out 5.

$$5\left(a^{3}b^{6}-8x^{3}y^{6}\right)$$

Consider a^{3}b^{6}-8x^{3}y^{6}. Consider a^{3}b^{6}-8x^{3}y^{6} as a polynomial over variable a.

$$b^{6}a^{3}-8x^{3}y^{6}$$

Find one factor of the form b^{k}a^{m}+n, where b^{k}a^{m} divides the monomial with the highest power b^{6}a^{3} and n divides the constant factor -8x^{3}y^{6}. One such factor is -2xy^{2}+ab^{2}. Factor the polynomial by dividing it by this factor.

$$\left(-2xy^{2}+ab^{2}\right)\left(4x^{2}y^{4}+2axb^{2}y^{2}+a^{2}b^{4}\right)$$

Rewrite the complete factored expression.

$$5\left(-2xy^{2}+ab^{2}\right)\left(4x^{2}y^{4}+2axb^{2}y^{2}+a^{2}b^{4}\right)$$

Evaluate

$$5\left(a^{3}b^{6}-8x^{3}y^{6}\right)$$