Solve -x(x+5)(x-2)

$$- x ( x + 5 ) ( x - 2 )$$

Evaluate

$$-x\left(x-2\right)\left(x+5\right)$$

Solution Steps

Use the distributive property to multiply -x by x+5.

$$\left(\left(-x\right)x+5\left(-x\right)\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of \left(-x\right)x+5\left(-x\right) by each term of x-2.

$$\left(-x\right)x^{2}-2\left(-x\right)x+5\left(-x\right)x-10\left(-x\right)$$

Multiply -2 and -1 to get 2.

$$\left(-x\right)x^{2}+2xx+5\left(-x\right)x-10\left(-x\right)$$

Multiply x and x to get x^{2}.

$$\left(-x\right)x^{2}+2x^{2}+5\left(-x\right)x-10\left(-x\right)$$

Multiply -10 and -1 to get 10.

$$\left(-x\right)x^{2}+2x^{2}+5\left(-x\right)x+10x$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-x^{3}+2x^{2}+5\left(-1\right)xx+10x$$

Multiply x and x to get x^{2}.

$$-x^{3}+2x^{2}+5\left(-1\right)x^{2}+10x$$

Multiply 5 and -1 to get -5.

$$-x^{3}+2x^{2}-5x^{2}+10x$$

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

$$-x^{3}-3x^{2}+10x$$

Expand

$$10x-3x^{2}-x^{3}$$

Solution Steps

Use the distributive property to multiply -x by x+5.

$$\left(\left(-x\right)x+5\left(-x\right)\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of \left(-x\right)x+5\left(-x\right) by each term of x-2.

$$\left(-x\right)x^{2}-2\left(-x\right)x+5\left(-x\right)x-10\left(-x\right)$$

Multiply -2 and -1 to get 2.

$$\left(-x\right)x^{2}+2xx+5\left(-x\right)x-10\left(-x\right)$$

Multiply x and x to get x^{2}.

$$\left(-x\right)x^{2}+2x^{2}+5\left(-x\right)x-10\left(-x\right)$$

Multiply -10 and -1 to get 10.

$$\left(-x\right)x^{2}+2x^{2}+5\left(-x\right)x+10x$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-x^{3}+2x^{2}+5\left(-1\right)xx+10x$$

Multiply x and x to get x^{2}.

$$-x^{3}+2x^{2}+5\left(-1\right)x^{2}+10x$$

Multiply 5 and -1 to get -5.

$$-x^{3}+2x^{2}-5x^{2}+10x$$

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

$$-x^{3}-3x^{2}+10x$$