Solve m(m-7)-(7-m)(m-2)

$$m ( m - 7 ) - ( 7 - m ) ( m - 2 )$$

Evaluate

$$2\left(m-7\right)\left(m-1\right)$$

Solution Steps

Use the distributive property to multiply m by m-7.

$$m^{2}-7m-\left(7-m\right)\left(m-2\right)$$

Apply the distributive property by multiplying each term of 7-m by each term of m-2.

$$m^{2}-7m-\left(7m-14-m^{2}+2m\right)$$

Combine 7m and 2m to get 9m.

$$m^{2}-7m-\left(9m-14-m^{2}\right)$$

To find the opposite of 9m-14-m^{2}, find the opposite of each term.

$$m^{2}-7m-9m-\left(-14\right)-\left(-m^{2}\right)$$

The opposite of -14 is 14.

$$m^{2}-7m-9m+14-\left(-m^{2}\right)$$

The opposite of -m^{2} is m^{2}.

$$m^{2}-7m-9m+14+m^{2}$$

Combine -7m and -9m to get -16m.

$$m^{2}-16m+14+m^{2}$$

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

$$2m^{2}-16m+14$$

Expand

$$2m^{2}-16m+14$$

Solution Steps

Use the distributive property to multiply m by m-7.

$$m^{2}-7m-\left(7-m\right)\left(m-2\right)$$

Apply the distributive property by multiplying each term of 7-m by each term of m-2.

$$m^{2}-7m-\left(7m-14-m^{2}+2m\right)$$

Combine 7m and 2m to get 9m.

$$m^{2}-7m-\left(9m-14-m^{2}\right)$$

To find the opposite of 9m-14-m^{2}, find the opposite of each term.

$$m^{2}-7m-9m-\left(-14\right)-\left(-m^{2}\right)$$

The opposite of -14 is 14.

$$m^{2}-7m-9m+14-\left(-m^{2}\right)$$

The opposite of -m^{2} is m^{2}.

$$m^{2}-7m-9m+14+m^{2}$$

Combine -7m and -9m to get -16m.

$$m^{2}-16m+14+m^{2}$$

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

$$2m^{2}-16m+14$$