Solve (7x^2-5x+8)-(3x^2-2x-5)-(x^2-4x+10)+(2x^2+3x-7)

$$( 7 x ^ { 2 } - 5 x + 8 ) - ( 3 x ^ { 2 } - 2 x - 5 ) - ( x ^ { 2 } - 4 x + 10 ) + ( 2 x ^ { 2 } + 3 x - 7 )$$

Evaluate

$$5x^{2}+4x-4$$

Solution Steps

To find the opposite of 3x^{2}-2x-5, find the opposite of each term.

$$7x^{2}-5x+8-3x^{2}+2x+5-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

Combine 7x^{2} and -3x^{2} to get 4x^{2}.

$$4x^{2}-5x+8+2x+5-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

Combine -5x and 2x to get -3x.

$$4x^{2}-3x+8+5-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

Add 8 and 5 to get 13.

$$4x^{2}-3x+13-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

To find the opposite of x^{2}-4x+10, find the opposite of each term.

$$4x^{2}-3x+13-x^{2}+4x-10+2x^{2}+3x-7$$

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

$$3x^{2}-3x+13+4x-10+2x^{2}+3x-7$$

Combine -3x and 4x to get x.

$$3x^{2}+x+13-10+2x^{2}+3x-7$$

Subtract 10 from 13 to get 3.

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

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

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

Combine x and 3x to get 4x.

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

Subtract 7 from 3 to get -4.

$$5x^{2}+4x-4$$

Expand

$$5x^{2}+4x-4$$

Solution Steps

To find the opposite of 3x^{2}-2x-5, find the opposite of each term.

$$7x^{2}-5x+8-3x^{2}+2x+5-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

Combine 7x^{2} and -3x^{2} to get 4x^{2}.

$$4x^{2}-5x+8+2x+5-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

Combine -5x and 2x to get -3x.

$$4x^{2}-3x+8+5-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

Add 8 and 5 to get 13.

$$4x^{2}-3x+13-\left(x^{2}-4x+10\right)+2x^{2}+3x-7$$

To find the opposite of x^{2}-4x+10, find the opposite of each term.

$$4x^{2}-3x+13-x^{2}+4x-10+2x^{2}+3x-7$$

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

$$3x^{2}-3x+13+4x-10+2x^{2}+3x-7$$

Combine -3x and 4x to get x.

$$3x^{2}+x+13-10+2x^{2}+3x-7$$

Subtract 10 from 13 to get 3.

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

Combine 3x^{2} and 2x^{2} to get 5x^{2}.

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

Combine x and 3x to get 4x.

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

Subtract 7 from 3 to get -4.

$$5x^{2}+4x-4$$