Solve (1)(-2x)^5-(-x)^3*(-3x)^2

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

Evaluate

$$-23x^{5}$$

Solution Steps

Expand \left(-2x\right)^{5}.

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

Calculate -2 to the power of 5 and get -32.

$$1\left(-32\right)x^{5}-\left(-x\right)^{3}\left(-3x\right)^{2}$$

Multiply 1 and -32 to get -32.

$$-32x^{5}-\left(-x\right)^{3}\left(-3x\right)^{2}$$

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

$$-32x^{5}-\left(-x\right)^{3}\left(-3\right)^{2}x^{2}$$

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

$$-32x^{5}-\left(-x\right)^{3}\times 9x^{2}$$

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

$$-32x^{5}-\left(-1\right)^{3}x^{3}\times 9x^{2}$$

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

$$-32x^{5}-\left(-x^{3}\times 9x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$-32x^{5}+x^{3}\times 9x^{2}$$

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

$$-32x^{5}+x^{5}\times 9$$

Combine -32x^{5} and x^{5}\times 9 to get -23x^{5}.

$$-23x^{5}$$

Expand

$$-23x^{5}$$

Solution Steps

Expand \left(-2x\right)^{5}.

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

Calculate -2 to the power of 5 and get -32.

$$1\left(-32\right)x^{5}-\left(-x\right)^{3}\left(-3x\right)^{2}$$

Multiply 1 and -32 to get -32.

$$-32x^{5}-\left(-x\right)^{3}\left(-3x\right)^{2}$$

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

$$-32x^{5}-\left(-x\right)^{3}\left(-3\right)^{2}x^{2}$$

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

$$-32x^{5}-\left(-x\right)^{3}\times 9x^{2}$$

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

$$-32x^{5}-\left(-1\right)^{3}x^{3}\times 9x^{2}$$

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

$$-32x^{5}-\left(-x^{3}\times 9x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$-32x^{5}+x^{3}\times 9x^{2}$$

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

$$-32x^{5}+x^{5}\times 9$$

Combine -32x^{5} and x^{5}\times 9 to get -23x^{5}.

$$-23x^{5}$$