Question

Factor ^2 - 4x + 4. x^2 - 4x +4=

Answer 1

Answer:  (x-2)(x-2)

This is the same as $(x-2)^2$

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Explanation:

The middle coefficient is -4 and the last term is 4.

We need to find factors of the last term that add to the middle coefficient.

Here is a list of all ways to multiply two integers to get 4, and the sum of each pair of factors.

• -1 + (-4) = -5
• -2 + (-2) = -4
• 2 + 2 = 4
• 1 + 4 = 5

The second row of that list above is what we're after. So

-2 + (-2) = -4

-2 * (-2) = 4

Meaning the factorization is (x-2)(x-2). Note the "-2" values in each factor

We can use the FOIL rule or distribution to go from (x-2)(x-2) back to x^2-4x+4 to confirm the answer.