Simplify (2m-9)^2

${(2 m - 9)}^{2}$

Step 1

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

$(2 m - 9) (2 m - 9)$

Step 2

Expand $(2 m - 9) (2 m - 9)$ using the FOIL Method.

Apply the distributive property.

$2 m (2 m - 9) - 9 (2 m - 9)$

Apply the distributive property.

$2 m (2 m) + 2 m \cdot - 9 - 9 (2 m - 9)$

Apply the distributive property.

$2 m (2 m) + 2 m \cdot - 9 - 9 (2 m) - 9 \cdot - 9$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 m \cdot m + 2 m \cdot - 9 - 9 (2 m) - 9 \cdot - 9$

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

Move $m$ .

$2 \cdot 2 (m \cdot m) + 2 m \cdot - 9 - 9 (2 m) - 9 \cdot - 9$

Multiply $m$ by $m$ .

$2 \cdot 2 m^{2} + 2 m \cdot - 9 - 9 (2 m) - 9 \cdot - 9$

Multiply $2$ by $2$ .

$4 m^{2} + 2 m \cdot - 9 - 9 (2 m) - 9 \cdot - 9$

Multiply $- 9$ by $2$ .

$4 m^{2} - 18 m - 9 (2 m) - 9 \cdot - 9$

Multiply $2$ by $- 9$ .

$4 m^{2} - 18 m - 18 m - 9 \cdot - 9$

Multiply $- 9$ by $- 9$ .

$4 m^{2} - 18 m - 18 m + 81$

Subtract $18 m$ from $- 18 m$ .

$4 m^{2} - 36 m + 81$