Solve (-x+1)(x^2+4x-15)

$$(-x+1)( { x }^{ 2 } +4x-15)$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -x+1 by x^{2}+4x-15.

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

Multiply -15 and -1 to get 15.

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

Combine 15x and 4x to get 19x.

$$\left(-x\right)x^{2}+4\left(-x\right)x+19x+x^{2}-15$$

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

$$-x^{3}+4\left(-1\right)xx+19x+x^{2}-15$$

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

$$-x^{3}+4\left(-1\right)x^{2}+19x+x^{2}-15$$

Multiply 4 and -1 to get -4.

$$-x^{3}-4x^{2}+19x+x^{2}-15$$

Combine -4x^{2} and x^{2} to get -3x^{2}.

$$-x^{3}-3x^{2}+19x-15$$

Expand

$$-x^{3}-3x^{2}+19x-15$$

Solution Steps

Use the distributive property to multiply -x+1 by x^{2}+4x-15.

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

Multiply -15 and -1 to get 15.

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

Combine 15x and 4x to get 19x.

$$\left(-x\right)x^{2}+4\left(-x\right)x+19x+x^{2}-15$$

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

$$-x^{3}+4\left(-1\right)xx+19x+x^{2}-15$$

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

$$-x^{3}+4\left(-1\right)x^{2}+19x+x^{2}-15$$

Multiply 4 and -1 to get -4.

$$-x^{3}-4x^{2}+19x+x^{2}-15$$

Combine -4x^{2} and x^{2} to get -3x^{2}.

$$-x^{3}-3x^{2}+19x-15$$