Evaluate (5-x)^2

${(5 - x)}^{2}$

Step 1

Rewrite ${(5 - x)}^{2}$ as $(5 - x) (5 - x)$ .

$(5 - x) (5 - x)$

Step 2

Expand $(5 - x) (5 - x)$ using the FOIL Method.

Apply the distributive property.

$5 (5 - x) - x (5 - x)$

Apply the distributive property.

$5 \cdot 5 + 5 (- x) - x (5 - x)$

Apply the distributive property.

$5 \cdot 5 + 5 (- x) - x \cdot 5 - x (- x)$

$5 \cdot 5 + 5 (- x) - x \cdot 5 - x (- x)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

$25 + 5 (- x) - x \cdot 5 - x (- x)$

Multiply $- 1$ by $5$ .

$25 - 5 x - x \cdot 5 - x (- x)$

Multiply $5$ by $- 1$ .

$25 - 5 x - 5 x - x (- x)$

Rewrite using the commutative property of multiplication.

$25 - 5 x - 5 x - 1 \cdot - 1 x \cdot x$

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

Move $x$ .

$25 - 5 x - 5 x - 1 \cdot - 1 (x \cdot x)$

Multiply $x$ by $x$ .

$25 - 5 x - 5 x - 1 \cdot - 1 x^{2}$

$25 - 5 x - 5 x - 1 \cdot - 1 x^{2}$

Multiply $- 1$ by $- 1$ .

$25 - 5 x - 5 x + 1 x^{2}$

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

$25 - 5 x - 5 x + x^{2}$

$25 - 5 x - 5 x + x^{2}$

Subtract $5 x$ from $- 5 x$ .

$25 - 10 x + x^{2}$

$25 - 10 x + x^{2}$

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