Evaluate (9+4m)^2

${(9 + 4 m)}^{2}$

Step 1

Rewrite ${(9 + 4 m)}^{2}$ as $(9 + 4 m) (9 + 4 m)$ .

$(9 + 4 m) (9 + 4 m)$

Step 2

Expand $(9 + 4 m) (9 + 4 m)$ using the FOIL Method.

Apply the distributive property.

$9 (9 + 4 m) + 4 m (9 + 4 m)$

Apply the distributive property.

$9 \cdot 9 + 9 (4 m) + 4 m (9 + 4 m)$

Apply the distributive property.

$9 \cdot 9 + 9 (4 m) + 4 m \cdot 9 + 4 m (4 m)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (4 m) + 4 m \cdot 9 + 4 m (4 m)$

Multiply $4$ by $9$ .

$81 + 36 m + 4 m \cdot 9 + 4 m (4 m)$

Multiply $9$ by $4$ .

$81 + 36 m + 36 m + 4 m (4 m)$

Rewrite using the commutative property of multiplication.

$81 + 36 m + 36 m + 4 \cdot 4 m \cdot m$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$81 + 36 m + 36 m + 4 \cdot 4 (m \cdot m)$

Multiply $m$ by $m$ .

$81 + 36 m + 36 m + 4 \cdot 4 m^{2}$

Multiply $4$ by $4$ .

$81 + 36 m + 36 m + 16 m^{2}$

Add $36 m$ and $36 m$ .

$81 + 72 m + 16 m^{2}$