Solve 2m(m-5)-(5-m)(m-6)

$$2 m ( m - 5 ) - ( 5 - m ) ( m - 6 )$$

Evaluate

$$3\left(m-5\right)\left(m-2\right)$$

Solution Steps

Use the distributive property to multiply 2m by m-5.

$$2m^{2}-10m-\left(5-m\right)\left(m-6\right)$$

Apply the distributive property by multiplying each term of 5-m by each term of m-6.

$$2m^{2}-10m-\left(5m-30-m^{2}+6m\right)$$

Combine 5m and 6m to get 11m.

$$2m^{2}-10m-\left(11m-30-m^{2}\right)$$

To find the opposite of 11m-30-m^{2}, find the opposite of each term.

$$2m^{2}-10m-11m-\left(-30\right)-\left(-m^{2}\right)$$

The opposite of -30 is 30.

$$2m^{2}-10m-11m+30-\left(-m^{2}\right)$$

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

$$2m^{2}-10m-11m+30+m^{2}$$

Combine -10m and -11m to get -21m.

$$2m^{2}-21m+30+m^{2}$$

Combine 2m^{2} and m^{2} to get 3m^{2}.

$$3m^{2}-21m+30$$

Expand

$$3m^{2}-21m+30$$

Solution Steps

Use the distributive property to multiply 2m by m-5.

$$2m^{2}-10m-\left(5-m\right)\left(m-6\right)$$

Apply the distributive property by multiplying each term of 5-m by each term of m-6.

$$2m^{2}-10m-\left(5m-30-m^{2}+6m\right)$$

Combine 5m and 6m to get 11m.

$$2m^{2}-10m-\left(11m-30-m^{2}\right)$$

To find the opposite of 11m-30-m^{2}, find the opposite of each term.

$$2m^{2}-10m-11m-\left(-30\right)-\left(-m^{2}\right)$$

The opposite of -30 is 30.

$$2m^{2}-10m-11m+30-\left(-m^{2}\right)$$

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

$$2m^{2}-10m-11m+30+m^{2}$$

Combine -10m and -11m to get -21m.

$$2m^{2}-21m+30+m^{2}$$

Combine 2m^{2} and m^{2} to get 3m^{2}.

$$3m^{2}-21m+30$$