Solve (-x^2-5x+2)(-x^3-3x)=

$$( - x ^ { 2 } - 5 x + 2 ) ( - x ^ { 3 } - 3 x ) =$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -x^{2}-5x+2 by -x^{3}-3x.

$$\left(-x^{2}\right)\left(-x^{3}\right)-3\left(-x^{2}\right)x-5x\left(-x^{3}\right)+15x^{2}+2\left(-x^{3}\right)-6x$$

Multiply -3 and -1 to get 3.

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{2}x-5x\left(-x^{3}\right)+15x^{2}+2\left(-x^{3}\right)-6x$$

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

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{3}-5x\left(-x^{3}\right)+15x^{2}+2\left(-x^{3}\right)-6x$$

Multiply -5 and -1 to get 5.

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{3}+5xx^{3}+15x^{2}+2\left(-x^{3}\right)-6x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{3}+5x^{4}+15x^{2}+2\left(-x^{3}\right)-6x$$

Multiply -1 and -1 to get 1.

$$x^{2}x^{3}+3x^{3}+5x^{4}+15x^{2}+2\left(-1\right)x^{3}-6x$$

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

$$x^{5}+3x^{3}+5x^{4}+15x^{2}+2\left(-1\right)x^{3}-6x$$

Multiply 2 and -1 to get -2.

$$x^{5}+3x^{3}+5x^{4}+15x^{2}-2x^{3}-6x$$

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

$$x^{5}+x^{3}+5x^{4}+15x^{2}-6x$$

Expand

$$x^{5}+5x^{4}+x^{3}+15x^{2}-6x$$

Solution Steps

Use the distributive property to multiply -x^{2}-5x+2 by -x^{3}-3x.

$$\left(-x^{2}\right)\left(-x^{3}\right)-3\left(-x^{2}\right)x-5x\left(-x^{3}\right)+15x^{2}+2\left(-x^{3}\right)-6x$$

Multiply -3 and -1 to get 3.

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{2}x-5x\left(-x^{3}\right)+15x^{2}+2\left(-x^{3}\right)-6x$$

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

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{3}-5x\left(-x^{3}\right)+15x^{2}+2\left(-x^{3}\right)-6x$$

Multiply -5 and -1 to get 5.

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{3}+5xx^{3}+15x^{2}+2\left(-x^{3}\right)-6x$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(-x^{2}\right)\left(-x^{3}\right)+3x^{3}+5x^{4}+15x^{2}+2\left(-x^{3}\right)-6x$$

Multiply -1 and -1 to get 1.

$$x^{2}x^{3}+3x^{3}+5x^{4}+15x^{2}+2\left(-1\right)x^{3}-6x$$

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

$$x^{5}+3x^{3}+5x^{4}+15x^{2}+2\left(-1\right)x^{3}-6x$$

Multiply 2 and -1 to get -2.

$$x^{5}+3x^{3}+5x^{4}+15x^{2}-2x^{3}-6x$$

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

$$x^{5}+x^{3}+5x^{4}+15x^{2}-6x$$