Solve 1/2(m^2+m+1)-(4m^2-4m+2)

$$\frac { 1 } { 2 } ( m ^ { 2 } + m + 1 ) - ( 4 m ^ { 2 } - 4 m + 2 )$$

Evaluate

$$\frac{-7m^{2}+9m-3}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by m^{2}+m+1.

$$\frac{1}{2}m^{2}+\frac{1}{2}m+\frac{1}{2}-\left(4m^{2}-4m+2\right)$$

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

$$\frac{1}{2}m^{2}+\frac{1}{2}m+\frac{1}{2}-4m^{2}+4m-2$$

Combine \frac{1}{2}m^{2} and -4m^{2} to get -\frac{7}{2}m^{2}.

$$-\frac{7}{2}m^{2}+\frac{1}{2}m+\frac{1}{2}+4m-2$$

Combine \frac{1}{2}m and 4m to get \frac{9}{2}m.

$$-\frac{7}{2}m^{2}+\frac{9}{2}m+\frac{1}{2}-2$$

Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.

$$-\frac{7}{2}m^{2}+\frac{9}{2}m-\frac{3}{2}$$

Expand

$$\frac{-7m^{2}+9m-3}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by m^{2}+m+1.

$$\frac{1}{2}m^{2}+\frac{1}{2}m+\frac{1}{2}-\left(4m^{2}-4m+2\right)$$

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

$$\frac{1}{2}m^{2}+\frac{1}{2}m+\frac{1}{2}-4m^{2}+4m-2$$

Combine \frac{1}{2}m^{2} and -4m^{2} to get -\frac{7}{2}m^{2}.

$$-\frac{7}{2}m^{2}+\frac{1}{2}m+\frac{1}{2}+4m-2$$

Combine \frac{1}{2}m and 4m to get \frac{9}{2}m.

$$-\frac{7}{2}m^{2}+\frac{9}{2}m+\frac{1}{2}-2$$

Subtract 2 from \frac{1}{2} to get -\frac{3}{2}.

$$-\frac{7}{2}m^{2}+\frac{9}{2}m-\frac{3}{2}$$