Solve 5a^{5}b^{2}-8a^4b^3+3a^3b^4

$$5 a ^ { 5 } b ^ { 2 } - 8 a ^ { 4 } b ^ { 3 } + 3 a ^ { 3 } b ^ { 4 }$$

Factor

$$\left(a-b\right)\left(5a-3b\right)b^{2}a^{3}$$

Solution Steps

Factor out a^{3}b^{2}.

$$a^{3}b^{2}\left(5a^{2}-8ab+3b^{2}\right)$$

Consider 5a^{2}-8ab+3b^{2}. Consider 5a^{2}-8ab+3b^{2} as a polynomial over variable a.

$$5a^{2}-8ba+3b^{2}$$

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 5a^{2} and n divides the constant factor 3b^{2}. One such factor is 5a-3b. Factor the polynomial by dividing it by this factor.

$$\left(5a-3b\right)\left(a-b\right)$$

Rewrite the complete factored expression.

$$a^{3}b^{2}\left(5a-3b\right)\left(a-b\right)$$

Evaluate

$$\left(a-b\right)\left(5a-3b\right)b^{2}a^{3}$$