Solve 20-45(m+n)^2

$$20 - 45 ( m + n ) ^ { 2 }$$

Evaluate

$$-45\left(m+n\right)^{2}+20$$

Solution Steps

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

$$20-45\left(m^{2}+2mn+n^{2}\right)$$

Use the distributive property to multiply -45 by m^{2}+2mn+n^{2}.

$$20-45m^{2}-90mn-45n^{2}$$

Expand

$$20-45n^{2}-90mn-45m^{2}$$

Solution Steps

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

$$20-45\left(m^{2}+2mn+n^{2}\right)$$

Use the distributive property to multiply -45 by m^{2}+2mn+n^{2}.

$$20-45m^{2}-90mn-45n^{2}$$