Solve (-x^2+4x-7)*(2x^2+5x+1)=

$$( - x ^ { 2 } + 4 x - 7 ) \cdot ( 2 x ^ { 2 } + 5 x + 1 ) =$$

Evaluate

$$\left(-x^{2}+4x-7\right)\left(2x^{2}+5x+1\right)$$

Solution Steps

Use the distributive property to multiply -x^{2}+4x-7 by 2x^{2}+5x+1 and combine like terms.

$$2\left(-x^{2}\right)x^{2}+5\left(-x^{2}\right)x-x^{2}+8x^{3}+6x^{2}-31x-7$$

Multiply 2 and -1 to get -2.

$$-2x^{2}x^{2}+5\left(-1\right)x^{2}x-x^{2}+8x^{3}+6x^{2}-31x-7$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-2x^{4}+5\left(-1\right)x^{2}x-x^{2}+8x^{3}+6x^{2}-31x-7$$

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

$$-2x^{4}+5\left(-1\right)x^{3}-x^{2}+8x^{3}+6x^{2}-31x-7$$

Multiply 5 and -1 to get -5.

$$-2x^{4}-5x^{3}-x^{2}+8x^{3}+6x^{2}-31x-7$$

Combine -5x^{3} and 8x^{3} to get 3x^{3}.

$$-2x^{4}+3x^{3}-x^{2}+6x^{2}-31x-7$$

Combine -x^{2} and 6x^{2} to get 5x^{2}.

$$-2x^{4}+3x^{3}+5x^{2}-31x-7$$

Expand

$$-2x^{4}+3x^{3}+5x^{2}-31x-7$$

Solution Steps

Use the distributive property to multiply -x^{2}+4x-7 by 2x^{2}+5x+1 and combine like terms.

$$2\left(-x^{2}\right)x^{2}+5\left(-x^{2}\right)x-x^{2}+8x^{3}+6x^{2}-31x-7$$

Multiply 2 and -1 to get -2.

$$-2x^{2}x^{2}+5\left(-1\right)x^{2}x-x^{2}+8x^{3}+6x^{2}-31x-7$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$-2x^{4}+5\left(-1\right)x^{2}x-x^{2}+8x^{3}+6x^{2}-31x-7$$

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

$$-2x^{4}+5\left(-1\right)x^{3}-x^{2}+8x^{3}+6x^{2}-31x-7$$

Multiply 5 and -1 to get -5.

$$-2x^{4}-5x^{3}-x^{2}+8x^{3}+6x^{2}-31x-7$$

Combine -5x^{3} and 8x^{3} to get 3x^{3}.

$$-2x^{4}+3x^{3}-x^{2}+6x^{2}-31x-7$$

Combine -x^{2} and 6x^{2} to get 5x^{2}.

$$-2x^{4}+3x^{3}+5x^{2}-31x-7$$