Solve 2u^2*10u^6+2u^2*9u^4

$$2 u ^ { 2 } \times 10 u ^ { 6 } + 2 u ^ { 2 } \times 9 u ^ { 4 }$$

Evaluate

$$20u^{8}+18u^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$2u^{8}\times 10+2u^{2}\times 9u^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$2u^{8}\times 10+2u^{6}\times 9$$

Multiply 2 and 10 to get 20.

$$20u^{8}+2u^{6}\times 9$$

Multiply 2 and 9 to get 18.

$$20u^{8}+18u^{6}$$

Factor

$$2\left(10u^{2}+9\right)u^{6}$$

Solution Steps

Factor out 2.

$$2\left(10u^{2}u^{6}+9u^{2}u^{4}\right)$$

Consider 10u^{8}+9u^{6}. Factor out u^{6}.

$$u^{6}\left(10u^{2}+9\right)$$

Rewrite the complete factored expression. Polynomial 10u^{2}+9 is not factored since it does not have any rational roots.

$$2u^{6}\left(10u^{2}+9\right)$$