Solve 2x^3*(-x)^2-(-x^2)^2(1-3x)

$$2 x ^ { 3 } \cdot ( - x ) ^ { 2 } - ( - x ^ { 2 } ) ^ { 2 } ( 1 - 3 x )$$

Evaluate

$$\left(5x-1\right)x^{4}$$

Solution Steps

Calculate -x to the power of 2 and get x^{2}.

$$2x^{3}x^{2}-\left(-x^{2}\right)^{2}\left(1-3x\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$2x^{5}-\left(-x^{2}\right)^{2}\left(1-3x\right)$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$2x^{5}-\left(x^{2}\right)^{2}\left(1-3x\right)$$

Use the distributive property to multiply \left(x^{2}\right)^{2} by 1-3x.

$$2x^{5}-\left(\left(x^{2}\right)^{2}-3\left(x^{2}\right)^{2}x\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x^{5}-\left(x^{4}-3\left(x^{2}\right)^{2}x\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x^{5}-\left(x^{4}-3x^{4}x\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2x^{5}-\left(x^{4}-3x^{5}\right)$$

To find the opposite of x^{4}-3x^{5}, find the opposite of each term.

$$2x^{5}-x^{4}+3x^{5}$$

Combine 2x^{5} and 3x^{5} to get 5x^{5}.

$$5x^{5}-x^{4}$$

Expand

$$5x^{5}-x^{4}$$

Solution Steps

Calculate -x to the power of 2 and get x^{2}.

$$2x^{3}x^{2}-\left(-x^{2}\right)^{2}\left(1-3x\right)$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$2x^{5}-\left(-x^{2}\right)^{2}\left(1-3x\right)$$

Calculate -x^{2} to the power of 2 and get \left(x^{2}\right)^{2}.

$$2x^{5}-\left(x^{2}\right)^{2}\left(1-3x\right)$$

Use the distributive property to multiply \left(x^{2}\right)^{2} by 1-3x.

$$2x^{5}-\left(\left(x^{2}\right)^{2}-3\left(x^{2}\right)^{2}x\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x^{5}-\left(x^{4}-3\left(x^{2}\right)^{2}x\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x^{5}-\left(x^{4}-3x^{4}x\right)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2x^{5}-\left(x^{4}-3x^{5}\right)$$

To find the opposite of x^{4}-3x^{5}, find the opposite of each term.

$$2x^{5}-x^{4}+3x^{5}$$

Combine 2x^{5} and 3x^{5} to get 5x^{5}.

$$5x^{5}-x^{4}$$