Solve (9x^3-x^2-x-1/3)+(x^3+x^2+x+4/3)

$$( 9 x ^ { 3 } - x ^ { 2 } - x - \frac { 1 } { 3 } ) + ( x ^ { 3 } + x ^ { 2 } + x + \frac { 4 } { 3 } )$$

Evaluate

$$10x^{3}+1$$

Solution Steps

Combine 9x^{3} and x^{3} to get 10x^{3}.

$$10x^{3}-x^{2}-x-\frac{1}{3}+x^{2}+x+\frac{4}{3}$$

Combine -x^{2} and x^{2} to get 0.

$$10x^{3}-x-\frac{1}{3}+x+\frac{4}{3}$$

Combine -x and x to get 0.

$$10x^{3}-\frac{1}{3}+\frac{4}{3}$$

Add -\frac{1}{3} and \frac{4}{3} to get 1.

$$10x^{3}+1$$

Factor

$$10x^{3}+1$$

Solution Steps

Factor out \frac{1}{3}.

$$\frac{30x^{3}+3}{3}$$

Consider 27x^{3}-3x^{2}-3x-1+3x^{3}+3x^{2}+3x+4. Multiply and combine like terms.

$$30x^{3}+3$$

Consider 30x^{3}+3. Factor out 3.

$$3\left(10x^{3}+1\right)$$

Rewrite the complete factored expression.

$$10x^{3}+1$$