Evaluate (4-x)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- x) - x \cdot 4 - x (- x)$

Multiply $- 1$ by $4$ .

$16 - 4 x - x \cdot 4 - x (- x)$

Multiply $4$ by $- 1$ .

$16 - 4 x - 4 x - x (- x)$

Rewrite using the commutative property of multiplication.

$16 - 4 x - 4 x - 1 \cdot - 1 x \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$16 - 4 x - 4 x - 1 \cdot - 1 (x \cdot x)$

Multiply $x$ by $x$ .

$16 - 4 x - 4 x - 1 \cdot - 1 x^{2}$

$16 - 4 x - 4 x - 1 \cdot - 1 x^{2}$

Multiply $- 1$ by $- 1$ .

$16 - 4 x - 4 x + 1 x^{2}$

Multiply $x^{2}$ by $1$ .

$16 - 4 x - 4 x + x^{2}$

$16 - 4 x - 4 x + x^{2}$

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

$16 - 8 x + x^{2}$

$16 - 8 x + x^{2}$

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