Solve 2a^3+7ab^2-7a^2b-2b^3):(2a-b)

$$2 a ^ { 3 } + 7 a b ^ { 2 } - 7 a ^ { 2 } b - 2 b ^ { 3 } ) : ( 2 a - b )$$

Factor

$$\left(a-b\right)\left(a-2b\right)\left(2a-b\right)$$

Solution Steps

Consider 2a^{3}+7ab^{2}-7a^{2}b-2b^{3} as a polynomial over variable a.

$$2a^{3}-7ba^{2}+7b^{2}a-2b^{3}$$

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

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

Consider 2a-2b. Factor out 2.

$$2\left(a-b\right)$$

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

$$a^{2}-\frac{5ba}{2}+b^{2}$$

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

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

Rewrite the complete factored expression. Simplify.

$$\left(a-2b\right)\left(a-b\right)\left(2a-b\right)$$

Evaluate

$$\left(a-b\right)\left(a-2b\right)\left(2a-b\right)$$