Solve 56a^2b-8a^4-98b^2

$$56 a ^ { 2 } b - 8 a ^ { 4 } - 98 b ^ { 2 }$$

Factor

$$-2\left(2a^{2}-7b\right)^{2}$$

Solution Steps

Factor out 2.

$$2\left(28a^{2}b-4a^{4}-49b^{2}\right)$$

Consider 28a^{2}b-4a^{4}-49b^{2}. Consider 28a^{2}b-4a^{4}-49b^{2} as a polynomial over variable a.

$$-4a^{4}+28ba^{2}-49b^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -4a^{4} and n divides the constant factor -49b^{2}. One such factor is 2a^{2}-7b. Factor the polynomial by dividing it by this factor.

$$\left(2a^{2}-7b\right)\left(-2a^{2}+7b\right)$$

Rewrite the complete factored expression.

$$2\left(2a^{2}-7b\right)\left(-2a^{2}+7b\right)$$

Evaluate

$$-2\left(2a^{2}-7b\right)^{2}$$