Simplify 3(a-4b)^2

$3 {(a - 4 b)}^{2}$

Step 1

Rewrite ${(a - 4 b)}^{2}$ as $(a - 4 b) (a - 4 b)$ .

$3 ((a - 4 b) (a - 4 b))$

Step 2

Expand $(a - 4 b) (a - 4 b)$ using the FOIL Method.

Apply the distributive property.

$3 (a (a - 4 b) - 4 b (a - 4 b))$

Apply the distributive property.

$3 (a \cdot a + a (- 4 b) - 4 b (a - 4 b))$

Apply the distributive property.

$3 (a \cdot a + a (- 4 b) - 4 b a - 4 b (- 4 b))$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$3 (a^{2} + a (- 4 b) - 4 b a - 4 b (- 4 b))$

Rewrite using the commutative property of multiplication.

$3 (a^{2} - 4 a b - 4 b a - 4 b (- 4 b))$

Rewrite using the commutative property of multiplication.

$3 (a^{2} - 4 a b - 4 b a - 4 \cdot - 4 b \cdot b)$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$3 (a^{2} - 4 a b - 4 b a - 4 \cdot - 4 (b \cdot b))$

Multiply $b$ by $b$ .

$3 (a^{2} - 4 a b - 4 b a - 4 \cdot - 4 b^{2})$

Multiply $- 4$ by $- 4$ .

$3 (a^{2} - 4 a b - 4 b a + 16 b^{2})$

Subtract $4 b a$ from $- 4 a b$ .

Move $b$ .

$3 (a^{2} - 4 a b - 4 a b + 16 b^{2})$

Subtract $4 a b$ from $- 4 a b$ .

$3 (a^{2} - 8 a b + 16 b^{2})$

Step 4

Apply the distributive property.

$3 a^{2} + 3 (- 8 a b) + 3 (16 b^{2})$

Step 5

Simplify.

Multiply $- 8$ by $3$ .

$3 a^{2} - 24 (a b) + 3 (16 b^{2})$

Multiply $16$ by $3$ .

$3 a^{2} - 24 (a b) + 48 b^{2}$

$3 a^{2} - 24 a b + 48 b^{2}$