Solve (-3x^{3})^{2}-(-x^2)^3+(-2x)^2-(-x)^3

$$( - 3 x ^ { 3 } ) ^ { 2 } - ( - x ^ { 2 } ) ^ { 3 } + ( - 2 x ) ^ { 2 } - ( - x ) ^ { 3 }$$

Evaluate

$$x^{2}\left(10x^{4}+x+4\right)$$

Solution Steps

Expand \left(-3x^{3}\right)^{2}.

$$\left(-3\right)^{2}\left(x^{3}\right)^{2}-\left(-x^{2}\right)^{3}+\left(-2x\right)^{2}-\left(-x\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(-3\right)^{2}x^{6}-\left(-x^{2}\right)^{3}+\left(-2x\right)^{2}-\left(-x\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$9x^{6}-\left(-x^{2}\right)^{3}+\left(-2x\right)^{2}-\left(-x\right)^{3}$$

Expand \left(-2x\right)^{2}.

$$9x^{6}-\left(-x^{2}\right)^{3}+\left(-2\right)^{2}x^{2}-\left(-x\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$9x^{6}-\left(-x^{2}\right)^{3}+4x^{2}-\left(-x\right)^{3}$$

Expand \left(-x^{2}\right)^{3}.

$$9x^{6}-\left(-1\right)^{3}\left(x^{2}\right)^{3}+4x^{2}-\left(-x\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$9x^{6}-\left(-1\right)^{3}x^{6}+4x^{2}-\left(-x\right)^{3}$$

Calculate -1 to the power of 3 and get -1.

$$9x^{6}-\left(-x^{6}\right)+4x^{2}-\left(-x\right)^{3}$$

Multiply -1 and -1 to get 1.

$$9x^{6}+x^{6}+4x^{2}-\left(-x\right)^{3}$$

Combine 9x^{6} and x^{6} to get 10x^{6}.

$$10x^{6}+4x^{2}-\left(-x\right)^{3}$$

Expand \left(-x\right)^{3}.

$$10x^{6}+4x^{2}-\left(-1\right)^{3}x^{3}$$

Calculate -1 to the power of 3 and get -1.

$$10x^{6}+4x^{2}-\left(-x^{3}\right)$$

Multiply -1 and -1 to get 1.

$$10x^{6}+4x^{2}+x^{3}$$

Expand

$$10x^{6}+x^{3}+4x^{2}$$

Solution Steps

Expand \left(-3x^{3}\right)^{2}.

$$\left(-3\right)^{2}\left(x^{3}\right)^{2}-\left(-x^{2}\right)^{3}+\left(-2x\right)^{2}-\left(-x\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(-3\right)^{2}x^{6}-\left(-x^{2}\right)^{3}+\left(-2x\right)^{2}-\left(-x\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$9x^{6}-\left(-x^{2}\right)^{3}+\left(-2x\right)^{2}-\left(-x\right)^{3}$$

Expand \left(-2x\right)^{2}.

$$9x^{6}-\left(-x^{2}\right)^{3}+\left(-2\right)^{2}x^{2}-\left(-x\right)^{3}$$

Calculate -2 to the power of 2 and get 4.

$$9x^{6}-\left(-x^{2}\right)^{3}+4x^{2}-\left(-x\right)^{3}$$

Expand \left(-x^{2}\right)^{3}.

$$9x^{6}-\left(-1\right)^{3}\left(x^{2}\right)^{3}+4x^{2}-\left(-x\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$9x^{6}-\left(-1\right)^{3}x^{6}+4x^{2}-\left(-x\right)^{3}$$

Calculate -1 to the power of 3 and get -1.

$$9x^{6}-\left(-x^{6}\right)+4x^{2}-\left(-x\right)^{3}$$

Multiply -1 and -1 to get 1.

$$9x^{6}+x^{6}+4x^{2}-\left(-x\right)^{3}$$

Combine 9x^{6} and x^{6} to get 10x^{6}.

$$10x^{6}+4x^{2}-\left(-x\right)^{3}$$

Expand \left(-x\right)^{3}.

$$10x^{6}+4x^{2}-\left(-1\right)^{3}x^{3}$$

Calculate -1 to the power of 3 and get -1.

$$10x^{6}+4x^{2}-\left(-x^{3}\right)$$

Multiply -1 and -1 to get 1.

$$10x^{6}+4x^{2}+x^{3}$$