Solve -2x^{3}(-x^4+3x^3-4x^2)+x^2=

$$- 2 x ^ { 3 } ( - x ^ { 4 } + 3 x ^ { 3 } - 4 x ^ { 2 } ) + x ^ { 2 } =$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -2x^{3} by -x^{4}+3x^{3}-4x^{2}.

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

Multiply -2 and -1 to get 2.

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

Expand

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

Solution Steps

Use the distributive property to multiply -2x^{3} by -x^{4}+3x^{3}-4x^{2}.

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

Multiply -2 and -1 to get 2.

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

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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