Solve 4xx-2x^3/2-3x^62x-4/6+x^2+x^7

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

Evaluate

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

Solution Steps

Cancel out 2, the greatest common factor in 4 and 2.

$$2\left(x-2x^{3}\right)x-3x^{6}\times \frac{2x-4}{6}+x^{2}+x^{7}$$

Cancel out 6, the greatest common factor in 3 and 6.

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

Divide each term of 2x-4 by 2 to get -2+x.

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

Use the distributive property to multiply -2+x by x^{6}.

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

To find the opposite of -2x^{6}+x^{7}, find the opposite of each term.

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

Combine -x^{7} and x^{7} to get 0.

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

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

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

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

$$2x^{2}-4x^{4}+2x^{6}+x^{2}$$

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

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

Expand

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

Solution Steps

Cancel out 2, the greatest common factor in 4 and 2.

$$2\left(x-2x^{3}\right)x-3x^{6}\times \frac{2x-4}{6}+x^{2}+x^{7}$$

Cancel out 6, the greatest common factor in 3 and 6.

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

Divide each term of 2x-4 by 2 to get -2+x.

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

Use the distributive property to multiply -2+x by x^{6}.

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

To find the opposite of -2x^{6}+x^{7}, find the opposite of each term.

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

Combine -x^{7} and x^{7} to get 0.

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

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

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

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

$$2x^{2}-4x^{4}+2x^{6}+x^{2}$$

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

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