Simplify 3(x-4)^2

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

Step 1

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

$3 ((x - 4) (x - 4))$

Step 2

Expand $(x - 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$3 (x (x - 4) - 4 (x - 4))$

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$3 (x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4)$

Move $- 4$ to the left of $x$ .

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

Multiply $- 4$ by $- 4$ .

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

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

Subtract $4 x$ from $- 4 x$ .

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

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

Step 4

Apply the distributive property.

$3 x^{2} + 3 (- 8 x) + 3 \cdot 16$

Step 5

Simplify.

Multiply $- 8$ by $3$ .

$3 x^{2} - 24 x + 3 \cdot 16$

Multiply $3$ by $16$ .

$3 x^{2} - 24 x + 48$

$3 x^{2} - 24 x + 48$

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