Solve (2z^2+3z-23)-(-z^2-7z-1)+(6z^2+2z+8)

$$( 2 z ^ { 2 } + 3 z - 23 ) - ( - z ^ { 2 } - 7 z - 1 ) + ( 6 z ^ { 2 } + 2 z + 8 )$$

Evaluate

$$9z^{2}+12z-14$$

Solution Steps

To find the opposite of -z^{2}-7z-1, find the opposite of each term.

$$2z^{2}+3z-23-\left(-z^{2}\right)+7z+1+6z^{2}+2z+8$$

Combine 3z and 7z to get 10z.

$$2z^{2}+10z-23-\left(-z^{2}\right)+1+6z^{2}+2z+8$$

Add -23 and 1 to get -22.

$$2z^{2}+10z-22-\left(-z^{2}\right)+6z^{2}+2z+8$$

Combine 2z^{2} and 6z^{2} to get 8z^{2}.

$$8z^{2}+10z-22-\left(-z^{2}\right)+2z+8$$

Combine 10z and 2z to get 12z.

$$8z^{2}+12z-22-\left(-z^{2}\right)+8$$

Add -22 and 8 to get -14.

$$8z^{2}+12z-14-\left(-z^{2}\right)$$

Multiply -1 and -1 to get 1.

$$8z^{2}+12z-14+z^{2}$$

Combine 8z^{2} and z^{2} to get 9z^{2}.

$$9z^{2}+12z-14$$

Expand

$$9z^{2}+12z-14$$

Solution Steps

To find the opposite of -z^{2}-7z-1, find the opposite of each term.

$$2z^{2}+3z-23-\left(-z^{2}\right)+7z+1+6z^{2}+2z+8$$

Combine 3z and 7z to get 10z.

$$2z^{2}+10z-23-\left(-z^{2}\right)+1+6z^{2}+2z+8$$

Add -23 and 1 to get -22.

$$2z^{2}+10z-22-\left(-z^{2}\right)+6z^{2}+2z+8$$

Combine 2z^{2} and 6z^{2} to get 8z^{2}.

$$8z^{2}+10z-22-\left(-z^{2}\right)+2z+8$$

Combine 10z and 2z to get 12z.

$$8z^{2}+12z-22-\left(-z^{2}\right)+8$$

Add -22 and 8 to get -14.

$$8z^{2}+12z-14-\left(-z^{2}\right)$$

Multiply -1 and -1 to get 1.

$$8z^{2}+12z-14+z^{2}$$

Combine 8z^{2} and z^{2} to get 9z^{2}.

$$9z^{2}+12z-14$$