Solve for q (x-p)^2=q

${(x - p)}^{2} = q$

Rewrite the equation as $q = {(x - p)}^{2}$ .

$q = {(x - p)}^{2}$

Simplify ${(x - p)}^{2}$ .

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

$q = (x - p) (x - p)$

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

Apply the distributive property.

$q = x (x - p) - p (x - p)$

Apply the distributive property.

$q = x \cdot x + x (- p) - p (x - p)$

Apply the distributive property.

$q = x \cdot x + x (- p) - p x - p (- p)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$q = x^{2} + x (- p) - p x - p (- p)$

Rewrite using the commutative property of multiplication.

$q = x^{2} - x p - p x - p (- p)$

Rewrite using the commutative property of multiplication.

$q = x^{2} - x p - p x - 1 \cdot - 1 p \cdot p$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$q = x^{2} - x p - p x - 1 \cdot - 1 (p \cdot p)$

Multiply $p$ by $p$ .

$q = x^{2} - x p - p x - 1 \cdot - 1 p^{2}$

Multiply $- 1$ by $- 1$ .

$q = x^{2} - x p - p x + 1 p^{2}$

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

$q = x^{2} - x p - p x + p^{2}$

Subtract $p x$ from $- x p$ .

Move $x$ .

$q = x^{2} - p x - p x + p^{2}$

Subtract $p x$ from $- p x$ .

$q = x^{2} - 2 p x + p^{2}$