Solve 5*(a^{2})^{5}*a^2-(2a^2)+a^3*a^3

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

Evaluate

$$a^{2}\left(5a^{10}+a^{4}-2\right)$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$5a^{10}a^{2}-2a^{2}+a^{3}a^{3}$$

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

$$5a^{12}-2a^{2}+a^{3}a^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$5a^{12}-2a^{2}+a^{6}$$

Factor

$$a^{2}\left(5a^{10}+a^{4}-2\right)$$

Solution Steps

Factor out common term a^{2} by using distributive property.

$$a^{2}\left(5\left(a^{2}\right)^{5}-2+a^{4}\right)$$

Consider 5\left(a^{2}\right)^{5}-2+a^{4}. Simplify.

$$5a^{10}+a^{4}-2$$

Rewrite the complete factored expression. Polynomial 5a^{10}+a^{4}-2 is not factored since it does not have any rational roots.

$$a^{2}\left(5a^{10}+a^{4}-2\right)$$