Solve for: 9(m+n)^2-4(m-n)^2

Expression: $9{\left( m+n \right)}^{2}-4{\left( m-n \right)}^{2}$

Use ${\left( a+b \right)}^{2}={a}^{2}+2ab+{b}^{2}$ to expand the expression

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

Use ${\left( a-b \right)}^{2}={a}^{2}-2ab+{b}^{2}$ to expand the expression

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

Distribute $9$ through the parentheses

$9{m}^{2}+18mn+9{n}^{2}-4\left( {m}^{2}-2mn+{n}^{2} \right)$

Distribute $-4$ through the parentheses

$9{m}^{2}+18mn+9{n}^{2}-4{m}^{2}+8mn-4{n}^{2}$

Collect like terms

$5{m}^{2}+18mn+9{n}^{2}+8mn-4{n}^{2}$

Collect like terms

$5{m}^{2}+26mn+9{n}^{2}-4{n}^{2}$

Collect like terms

$5{m}^{2}+26mn+5{n}^{2}$