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

$$( m - 3 ) ( m + 3 ) + 2 ( m + 3 ) ^ { 2 }$$

Evaluate

$$3\left(m+1\right)\left(m+3\right)$$

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}. Square 3.

$$m^{2}-9+2\left(m+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+3\right)^{2}.

$$m^{2}-9+2\left(m^{2}+6m+9\right)$$

Use the distributive property to multiply 2 by m^{2}+6m+9.

$$m^{2}-9+2m^{2}+12m+18$$

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

$$3m^{2}-9+12m+18$$

Add -9 and 18 to get 9.

$$3m^{2}+9+12m$$

Expand

$$3m^{2}+12m+9$$

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}. Square 3.

$$m^{2}-9+2\left(m+3\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(m+3\right)^{2}.

$$m^{2}-9+2\left(m^{2}+6m+9\right)$$

Use the distributive property to multiply 2 by m^{2}+6m+9.

$$m^{2}-9+2m^{2}+12m+18$$

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

$$3m^{2}-9+12m+18$$

Add -9 and 18 to get 9.

$$3m^{2}+9+12m$$