Solve f(x)=-x(x-3)(x+2)

$$f ( x ) = - x ( x - 3 ) ( x + 2 )$$

Evaluate

$$-x\left(x-3\right)\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply -x by x-3.

$$\left(\left(-x\right)x-3\left(-x\right)\right)\left(x+2\right)$$

Multiply -3 and -1 to get 3.

$$\left(\left(-x\right)x+3x\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of \left(-x\right)x+3x by each term of x+2.

$$\left(-x\right)x^{2}+2\left(-x\right)x+3x^{2}+6x$$

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

$$-x^{3}+2\left(-1\right)xx+3x^{2}+6x$$

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

$$-x^{3}+2\left(-1\right)x^{2}+3x^{2}+6x$$

Multiply 2 and -1 to get -2.

$$-x^{3}-2x^{2}+3x^{2}+6x$$

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

$$-x^{3}+x^{2}+6x$$

Expand

$$6x+x^{2}-x^{3}$$

Solution Steps

Use the distributive property to multiply -x by x-3.

$$\left(\left(-x\right)x-3\left(-x\right)\right)\left(x+2\right)$$

Multiply -3 and -1 to get 3.

$$\left(\left(-x\right)x+3x\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of \left(-x\right)x+3x by each term of x+2.

$$\left(-x\right)x^{2}+2\left(-x\right)x+3x^{2}+6x$$

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

$$-x^{3}+2\left(-1\right)xx+3x^{2}+6x$$

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

$$-x^{3}+2\left(-1\right)x^{2}+3x^{2}+6x$$

Multiply 2 and -1 to get -2.

$$-x^{3}-2x^{2}+3x^{2}+6x$$

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

$$-x^{3}+x^{2}+6x$$