Solve (m-3)(m+3)-m(m+2)

$$( m - 3 ) ( m + 3 ) - m ( m + 2 )$$

Evaluate

$$-2m-9$$

Solution Steps

Consider \left(m-3\right)\left(m+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$m^{2}-3^{2}-m\left(m+2\right)$$

Calculate 3 to the power of 2 and get 9.

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

Use the distributive property to multiply m by m+2.

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

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

$$m^{2}-9-m^{2}-2m$$

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

$$-9-2m$$

Expand

$$-2m-9$$

Solution Steps

Consider \left(m-3\right)\left(m+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$m^{2}-3^{2}-m\left(m+2\right)$$

Calculate 3 to the power of 2 and get 9.

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

Use the distributive property to multiply m by m+2.

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

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

$$m^{2}-9-m^{2}-2m$$

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

$$-9-2m$$