Solve {l}{(-2x)^2-(-3x)}{-x^2*(-3x)^2-3x^2}

$$\left. \begin{array} { l } { ( - 2 x ) ^ { 2 } - ( - 3 x ) } \\ { - x ^ { 2 } \times ( - 3 x ) ^ { 2 } - 3 x ^ { 2 } } \end{array} \right.$$

Evaluate

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

Solution Steps

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

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

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

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

The opposite of -3x is 3x.

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

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

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

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

$$4x^{2}+3x-x^{2}\times 9x^{2}-3x^{2}$$

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

$$4x^{2}+3x-x^{4}\times 9-3x^{2}$$

Multiply -1 and 9 to get -9.

$$4x^{2}+3x-9x^{4}-3x^{2}$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$x^{2}+3x-9x^{4}$$

Expand

$$3x+x^{2}-9x^{4}$$

Solution Steps

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

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

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

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

The opposite of -3x is 3x.

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

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

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

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

$$4x^{2}+3x-x^{2}\times 9x^{2}-3x^{2}$$

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

$$4x^{2}+3x-x^{4}\times 9-3x^{2}$$

Multiply -1 and 9 to get -9.

$$4x^{2}+3x-9x^{4}-3x^{2}$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$x^{2}+3x-9x^{4}$$