Solve ((3x^2-4x^2+5)-(x^2*x-2x^2+3x-4))-(3{x}^2*x-{x}^2-x+2)

$$((3 { x }^{ 2 } -4 { x }^{ 2 } +5)-( { x }^{ 2 } \times x-2 { x }^{ 2 } +3x-4))-(3 { x }^{ 2 } \times x- { x }^{ 2 } -x+2)$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

To find the opposite of x^{3}-2x^{2}+3x-4, find the opposite of each term.

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

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

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

Add 5 and 4 to get 9.

$$x^{2}+9-x^{3}-3x-\left(3x^{3}-x^{2}-x+2\right)$$

To find the opposite of 3x^{3}-x^{2}-x+2, find the opposite of each term.

$$x^{2}+9-x^{3}-3x-3x^{3}+x^{2}+x-2$$

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

$$x^{2}+9-4x^{3}-3x+x^{2}+x-2$$

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

$$2x^{2}+9-4x^{3}-3x+x-2$$

Combine -3x and x to get -2x.

$$2x^{2}+9-4x^{3}-2x-2$$

Subtract 2 from 9 to get 7.

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

Expand

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

Solution Steps

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

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

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

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

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

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

To find the opposite of x^{3}-2x^{2}+3x-4, find the opposite of each term.

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

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

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

Add 5 and 4 to get 9.

$$x^{2}+9-x^{3}-3x-\left(3x^{3}-x^{2}-x+2\right)$$

To find the opposite of 3x^{3}-x^{2}-x+2, find the opposite of each term.

$$x^{2}+9-x^{3}-3x-3x^{3}+x^{2}+x-2$$

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

$$x^{2}+9-4x^{3}-3x+x^{2}+x-2$$

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

$$2x^{2}+9-4x^{3}-3x+x-2$$

Combine -3x and x to get -2x.

$$2x^{2}+9-4x^{3}-2x-2$$

Subtract 2 from 9 to get 7.

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