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Completing the Square

Completing the Square 1.1 - Solution

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Recall that the expansion of a squared binomial is called a perfect square trinomial. It is the pattern for expanding the square of a binomial of the form Note that if we identify the coefficient of the linear term we can divide it by to obtain Then, we can add or subtract as needed to get the equivalent for and factor the trinomial as the squared of a binomial. This is called completing the square. We can compare the given the expression to the pattern discussed. As we can see, in the given expression the corresponding value is Since its constant term is equal to already, it is a perfect square trinomial. Then, according to the pattern it can be factored as

The trinomial is a perfect square trinomial because it equals