Solve (m-1)(6-m)-(10-m)(m+10)

$$( m - 1 ) ( 6 - m ) - ( 10 - m ) ( m + 10 )$$

Evaluate

$$7m-106$$

Solution Steps

Apply the distributive property by multiplying each term of m-1 by each term of 6-m.

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

Combine 6m and m to get 7m.

$$7m-m^{2}-6-\left(10-m\right)\left(m+10\right)$$

Consider \left(10-m\right)\left(m+10\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$7m-m^{2}-6-\left(10^{2}-m^{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$7m-m^{2}-6-\left(100-m^{2}\right)$$

To find the opposite of 100-m^{2}, find the opposite of each term.

$$7m-m^{2}-6-100-\left(-m^{2}\right)$$

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

$$7m-m^{2}-6-100+m^{2}$$

Subtract 100 from -6 to get -106.

$$7m-m^{2}-106+m^{2}$$

Combine -m^{2} and m^{2} to get 0.

$$7m-106$$

Expand

$$7m-106$$

Solution Steps

Apply the distributive property by multiplying each term of m-1 by each term of 6-m.

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

Combine 6m and m to get 7m.

$$7m-m^{2}-6-\left(10-m\right)\left(m+10\right)$$

Consider \left(10-m\right)\left(m+10\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$7m-m^{2}-6-\left(10^{2}-m^{2}\right)$$

Calculate 10 to the power of 2 and get 100.

$$7m-m^{2}-6-\left(100-m^{2}\right)$$

To find the opposite of 100-m^{2}, find the opposite of each term.

$$7m-m^{2}-6-100-\left(-m^{2}\right)$$

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

$$7m-m^{2}-6-100+m^{2}$$

Subtract 100 from -6 to get -106.

$$7m-m^{2}-106+m^{2}$$

Combine -m^{2} and m^{2} to get 0.

$$7m-106$$