Solve (2)3a^2*a^3-2a^5diva^3=

$$( 2 ) 3 a ^ { 2 } \cdot a ^ { 3 } - 2 a ^ { 5 } \div a ^ { 3 } =$$

Evaluate

$$6a^{5}-2a^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$2\times 3a^{5}-\frac{2a^{5}}{a^{3}}$$

Multiply 2 and 3 to get 6.

$$6a^{5}-\frac{2a^{5}}{a^{3}}$$

Cancel out a^{3} in both numerator and denominator.

$$6a^{5}-2a^{2}$$

Factor

$$2a^{2}\left(3a^{3}-1\right)$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$factor(2\times 3a^{5}-\frac{2a^{5}}{a^{3}})$$

Multiply 2 and 3 to get 6.

$$factor(6a^{5}-\frac{2a^{5}}{a^{3}})$$

Cancel out a^{3} in both numerator and denominator.

$$factor(6a^{5}-2a^{2})$$

Factor out 2.

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

Consider 3a^{5}-a^{2}. Factor out a^{2}.

$$a^{2}\left(3a^{3}-1\right)$$

Rewrite the complete factored expression. Polynomial 3a^{3}-1 is not factored since it does not have any rational roots.

$$2a^{2}\left(3a^{3}-1\right)$$