Factor. z^2 - 4z + 4 ______

Determine Approach: Determine the approach to factor the quadratic expression z^2 - 4z + 4. We can use the perfect square trinomial formula, which is (a - b)^2 = a^2 - 2ab + b^2, because the quadratic appears to be a perfect square trinomial.Identify Terms: Identify the terms in the expression z^2 - 4z + 4 that correspond to a^2, 2ab, and b^2. a^2 = z^2 (which implies a = z) 2ab = 4z (which implies 2 * a * b = 4z, so b must be 2 since a = z) b^2 = 4 (which implies b = 2) Check if the expression fits the perfect square trinomial pattern: (z - 2)^2 = z^2 - 4z + 4.Check Pattern: Write the factored form using the perfect square trinomial pattern. Since the expression fits the pattern, we can write it as (z - 2)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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z^2 - 4z + 4

Determine Approach: Determine the approach to factor the quadratic expression $z^2 - 4z + 4$ . We can use the perfect square trinomial formula, which is $(a - b)^2 = a^2 - 2ab + b^2$ , because the quadratic appears to be a perfect square trinomial.
Identify Terms: Identify the terms in the expression $z^2 - 4z + 4$ that correspond to $a^2$ , $2ab$ , and $b^2$ .
$a^2 = z^2$ (which implies $a = z$ )
$2ab = 4z$ (which implies $2 \cdot a \cdot b = 4z$ , so $b$ must be $2$ since $a = z$ )
$a^2$ $1$ (which implies $a^2$ $2$ )
Check if the expression fits the perfect square trinomial pattern: $a^2$ $3$ .
Check Pattern: Write the factored form using the perfect square trinomial pattern. $\newline$ Since the expression fits the pattern, we can write it as $(z - 2)^2$ .