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Chapter 0: Problem 50

Factor each perfect square trinomial. $$x^{2}+4 x+4$$

Short Answer

Expert verified
The perfect square trinomial \(x^{2} + 4x + 4\) factors to \((x + 2)^2\).

Step by step solution

01

Identify the square terms

Firstly, identify the square terms in the trinomial. Here, \(x^{2}\) is the square of \(x\), and \(4\) is the square of \(2\). Therefore \(a = x\) and \(b = 2\).
02

Verify double product term

Our next step will be to verify if the middle term in the trinomial is twice the product of the square root terms. Here \(2ab\) should equal \(4x\). If we multiply 2, \(a (x)\), and \(b (2)\), we get \(4x\), which is our middle term. This shows that the trinomial follows the pattern of a perfect square trinomial.
03

Factorize the trinomial

With Step 1 and Step 2 confirmed, we can factor the trinomial using the identity \((a + b)^2\). Thus, the trinomial \(x^{2} + 4x + 4\) can be factored to become \((x + 2)^2\).

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