Precalculus Examples

Determine if the Expression is a Perfect Square
Step 1
A trinomial can be a perfect square if it satisfies the following:
The first term is a perfect square.
The third term is a perfect square.
The middle term is either or times the product of the square root of the first term and the square root of the third term.
Step 2
Pull terms out from under the radical, assuming positive real numbers.
Step 3
Find , which is the square root of the third term . The square root of the third term is , so the third term is a perfect square.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Step 4
The first term is a perfect square. The third term is a perfect square. The middle term is times the product of the square root of the first term and the square root of the third term .
The polynomial is a perfect square.
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