Solve a^4+3a^2b-40b^2

$$a ^ { 4 } + 3 a ^ { 2 } b - 40 b ^ { 2 }$$

Factor

$$\left(a^{2}-5b\right)\left(a^{2}+8b\right)$$

Solution Steps

Consider a^{4}+3a^{2}b-40b^{2} as a polynomial over variable a.

$$a^{4}+3ba^{2}-40b^{2}$$

Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{4} and m divides the constant factor -40b^{2}. One such factor is a^{2}+8b. Factor the polynomial by dividing it by this factor.

$$\left(a^{2}+8b\right)\left(a^{2}-5b\right)$$

Evaluate

$$\left(a^{2}-5b\right)\left(a^{2}+8b\right)$$