Simplify (3-4m)^2

${(3 - 4 m)}^{2}$

Step 1

Rewrite ${(3 - 4 m)}^{2}$ as $(3 - 4 m) (3 - 4 m)$ .

$(3 - 4 m) (3 - 4 m)$

Step 2

Expand $(3 - 4 m) (3 - 4 m)$ using the FOIL Method.

Apply the distributive property.

$3 (3 - 4 m) - 4 m (3 - 4 m)$

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 m) - 4 m (3 - 4 m)$

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 m) - 4 m \cdot 3 - 4 m (- 4 m)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (- 4 m) - 4 m \cdot 3 - 4 m (- 4 m)$

Multiply $- 4$ by $3$ .

$9 - 12 m - 4 m \cdot 3 - 4 m (- 4 m)$

Multiply $3$ by $- 4$ .

$9 - 12 m - 12 m - 4 m (- 4 m)$

Rewrite using the commutative property of multiplication.

$9 - 12 m - 12 m - 4 \cdot - 4 m \cdot m$

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

Move $m$ .

$9 - 12 m - 12 m - 4 \cdot - 4 (m \cdot m)$

Multiply $m$ by $m$ .

$9 - 12 m - 12 m - 4 \cdot - 4 m^{2}$

Multiply $- 4$ by $- 4$ .

$9 - 12 m - 12 m + 16 m^{2}$

Subtract $12 m$ from $- 12 m$ .

$9 - 24 m + 16 m^{2}$