Find the Product (m+n)^2

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

Step 1

Rewrite ${(m + n)}^{2}$ as $(m + n) (m + n)$ .

$(m + n) (m + n)$

Step 2

Expand $(m + n) (m + n)$ using the FOIL Method.

Apply the distributive property.

$m (m + n) + n (m + n)$

Apply the distributive property.

$m \cdot m + m n + n (m + n)$

Apply the distributive property.

$m \cdot m + m n + n m + n \cdot n$

$m \cdot m + m n + n m + n \cdot n$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $m$ by $m$ .

$m^{2} + m n + n m + n \cdot n$

Multiply $n$ by $n$ .

$m^{2} + m n + n m + n^{2}$

$m^{2} + m n + n m + n^{2}$

Add $m n$ and $n m$ .

Reorder $n$ and $m$ .

$m^{2} + m n + m n + n^{2}$

Add $m n$ and $m n$ .

$m^{2} + 2 m n + n^{2}$

$m^{2} + 2 m n + n^{2}$

$m^{2} + 2 m n + n^{2}$

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