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

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

Evaluate

$$3m\left(m-6n\right)$$

Solution Steps

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

$$4m^{2}-12mn+9n^{2}-\left(m+3n\right)^{2}$$

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

$$4m^{2}-12mn+9n^{2}-\left(m^{2}+6mn+9n^{2}\right)$$

To find the opposite of m^{2}+6mn+9n^{2}, find the opposite of each term.

$$4m^{2}-12mn+9n^{2}-m^{2}-6mn-9n^{2}$$

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

$$3m^{2}-12mn+9n^{2}-6mn-9n^{2}$$

Combine -12mn and -6mn to get -18mn.

$$3m^{2}-18mn+9n^{2}-9n^{2}$$

Combine 9n^{2} and -9n^{2} to get 0.

$$3m^{2}-18mn$$

Expand

$$3m^{2}-18mn$$

Solution Steps

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

$$4m^{2}-12mn+9n^{2}-\left(m+3n\right)^{2}$$

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

$$4m^{2}-12mn+9n^{2}-\left(m^{2}+6mn+9n^{2}\right)$$

To find the opposite of m^{2}+6mn+9n^{2}, find the opposite of each term.

$$4m^{2}-12mn+9n^{2}-m^{2}-6mn-9n^{2}$$

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

$$3m^{2}-12mn+9n^{2}-6mn-9n^{2}$$

Combine -12mn and -6mn to get -18mn.

$$3m^{2}-18mn+9n^{2}-9n^{2}$$

Combine 9n^{2} and -9n^{2} to get 0.

$$3m^{2}-18mn$$