SOLUTION: Determine whether the following trinomial is a perfect square. x^2 + 4x + 4

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Question 774872: Determine whether the following trinomial is a perfect square. x^2 + 4x + 4
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A trinomial could be the square of a binomial
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2
(In words, the square of a binomial is the square of one term, plus the square of the other, plus their double product,
If we find two terms that are perfect squares, they could be the a%5E2 and b%5E2 in the "formula" above, and we would know what the a and b expressions are.
If it so happens the other term is twice the product of the a and b we figured out before, then the trinomial is a perfect square.

In x%5E2+%2B+4x+%2B+4, we find that
x%5E2 is the square of red%28x%29, and
4=2%2A2=2%5E2 is the square of blue%282%29.
We calculate twice the product of red%28x%29 and blue%282%29 as
2%2Ablue%282%29%2Ared%28x%29=4x and it is equal to the other term.
So x%5E2+%2B+4x+%2B+4=%28x%2B2%29%5E2
It is a perfect square.