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

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

Evaluate

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

Solution Steps

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

$$m^{2}-\left(4m^{2}+12m+9\right)$$

To find the opposite of 4m^{2}+12m+9, find the opposite of each term.

$$m^{2}-4m^{2}-12m-9$$

Combine m^{2} and -4m^{2} to get -3m^{2}.

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

Expand

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

Solution Steps

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

$$m^{2}-\left(4m^{2}+12m+9\right)$$

To find the opposite of 4m^{2}+12m+9, find the opposite of each term.

$$m^{2}-4m^{2}-12m-9$$

Combine m^{2} and -4m^{2} to get -3m^{2}.

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