Solve 16m^2-9(m+n)^2

$$16 m ^ { 2 } - 9 ( m + n ) ^ { 2 }$$

Evaluate

$$\left(m-3n\right)\left(7m+3n\right)$$

Solution Steps

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

$$16m^{2}-9\left(m^{2}+2mn+n^{2}\right)$$

Use the distributive property to multiply -9 by m^{2}+2mn+n^{2}.

$$16m^{2}-9m^{2}-18mn-9n^{2}$$

Combine 16m^{2} and -9m^{2} to get 7m^{2}.

$$7m^{2}-18mn-9n^{2}$$

Expand

$$7m^{2}-18mn-9n^{2}$$

Solution Steps

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

$$16m^{2}-9\left(m^{2}+2mn+n^{2}\right)$$

Use the distributive property to multiply -9 by m^{2}+2mn+n^{2}.

$$16m^{2}-9m^{2}-18mn-9n^{2}$$

Combine 16m^{2} and -9m^{2} to get 7m^{2}.

$$7m^{2}-18mn-9n^{2}$$