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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply -x by x-2.

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

Multiply -2 and -1 to get 2.

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

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

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

Multiply -5 and -1 to get 5.

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

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

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

Combine 5x^{2} and 2x^{2} to get 7x^{2}.

$$\left(-x\right)x^{2}+7x^{2}-10x$$

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

$$-x^{3}+7x^{2}-10x$$

Expand

$$-\left(x^{3}-7x^{2}+10x\right)$$

Solution Steps

Use the distributive property to multiply -x by x-2.

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

Multiply -2 and -1 to get 2.

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

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

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

Multiply -5 and -1 to get 5.

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

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

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

Combine 5x^{2} and 2x^{2} to get 7x^{2}.

$$\left(-x\right)x^{2}+7x^{2}-10x$$

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

$$-x^{3}+7x^{2}-10x$$