Solve for p p^2-4p+4=0

$p^{2} - 4 p + 4 = 0$

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$p^{2} - 4 p + 2^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 p = 2 \cdot p \cdot 2$

Rewrite the polynomial.

$p^{2} - 2 \cdot p \cdot 2 + 2^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = p$ and $b = 2$ .

${(p - 2)}^{2} = 0$

Set the $p - 2$ equal to $0$ .

$p - 2 = 0$

Add $2$ to both sides of the equation.

$p = 2$