Solve (-x^3+2x^2-5)(2x^2-3x+1)

$$( - x ^ { 3 } + 2 x ^ { 2 } - 5 ) ( 2 x ^ { 2 } - 3 x + 1 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -x^{3}+2x^{2}-5 by 2x^{2}-3x+1 and combine like terms.

$$2\left(-x^{3}\right)x^{2}-3\left(-x^{3}\right)x-x^{3}+4x^{4}-6x^{3}-8x^{2}+15x-5$$

Multiply -3 and -1 to get 3.

$$2\left(-x^{3}\right)x^{2}+3x^{3}x-x^{3}+4x^{4}-6x^{3}-8x^{2}+15x-5$$

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

$$2\left(-x^{3}\right)x^{2}+3x^{4}-x^{3}+4x^{4}-6x^{3}-8x^{2}+15x-5$$

Combine 3x^{4} and 4x^{4} to get 7x^{4}.

$$2\left(-x^{3}\right)x^{2}+7x^{4}-x^{3}-6x^{3}-8x^{2}+15x-5$$

Multiply 2 and -1 to get -2.

$$-2x^{3}x^{2}+7x^{4}-x^{3}-6x^{3}-8x^{2}+15x-5$$

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

$$-2x^{5}+7x^{4}-x^{3}-6x^{3}-8x^{2}+15x-5$$

Combine -x^{3} and -6x^{3} to get -7x^{3}.

$$-2x^{5}+7x^{4}-7x^{3}-8x^{2}+15x-5$$

Expand

$$-2x^{5}+7x^{4}-7x^{3}-8x^{2}+15x-5$$

Solution Steps

Use the distributive property to multiply -x^{3}+2x^{2}-5 by 2x^{2}-3x+1 and combine like terms.

$$2\left(-x^{3}\right)x^{2}-3\left(-x^{3}\right)x-x^{3}+4x^{4}-6x^{3}-8x^{2}+15x-5$$

Multiply -3 and -1 to get 3.

$$2\left(-x^{3}\right)x^{2}+3x^{3}x-x^{3}+4x^{4}-6x^{3}-8x^{2}+15x-5$$

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

$$2\left(-x^{3}\right)x^{2}+3x^{4}-x^{3}+4x^{4}-6x^{3}-8x^{2}+15x-5$$

Combine 3x^{4} and 4x^{4} to get 7x^{4}.

$$2\left(-x^{3}\right)x^{2}+7x^{4}-x^{3}-6x^{3}-8x^{2}+15x-5$$

Multiply 2 and -1 to get -2.

$$-2x^{3}x^{2}+7x^{4}-x^{3}-6x^{3}-8x^{2}+15x-5$$

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

$$-2x^{5}+7x^{4}-x^{3}-6x^{3}-8x^{2}+15x-5$$

Combine -x^{3} and -6x^{3} to get -7x^{3}.

$$-2x^{5}+7x^{4}-7x^{3}-8x^{2}+15x-5$$