Solve (m+n-9)(m+n+9)

$$( m + n - 9 ) ( m + n + 9 )$$

Evaluate

$$\left(m+n\right)^{2}-81$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=m+n and b=9.

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

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

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

Calculate 9 to the power of 2 and get 81.

$$m^{2}+2mn+n^{2}-81$$

Expand

$$m^{2}+2mn+n^{2}-81$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}, where a=m+n and b=9.

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

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

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

Calculate 9 to the power of 2 and get 81.

$$m^{2}+2mn+n^{2}-81$$