Questions: Factor the following trinomial. x² + 16x + 64 ([]x + [])² Enter

Solution Steps

To factor the given trinomial \( x^2 + 16x + 64 \), we need to recognize it as a perfect square trinomial. A perfect square trinomial takes the form \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, we identify \( a \) and \( b \) such that \( a^2 = x^2 \) and \( b^2 = 64 \), and then verify that \( 2ab = 16x \).

We start with the trinomial \( x^2 + 16x + 64 \).

We can express the trinomial in the form \( (a + b)^2 \). Here, we identify:

• \( a^2 = x^2 \) implies \( a = x \)
• \( b^2 = 64 \) implies \( b = 8 \)

We check if \( 2ab = 16x \): \[ 2ab = 2 \cdot x \cdot 8 = 16x \] This confirms that the trinomial is indeed a perfect square.

Thus, we can factor the trinomial as: \[ x^2 + 16x + 64 = (x + 8)^2 \]

Final Answer