Factor each difference of squares or perfect square trianomial W^2+16w+64

To factor the expression \(W^2 + 16W + 64\), we need to recognize it as a perfect square trinomial. A perfect square trinomial takes the form:

\[
a^2 + 2ab + b^2 = (a + b)^2
\]

In this case:

- The first term, \(W^2\), is a perfect square because \(W^2 = (W)^2\).
- The last term, \(64\), is a perfect square because \(64 = 8^2\).
- The middle term, \(16W\), should be equal to \(2ab\). Here, \(a = W\) and \(b = 8\), so \(2ab = 2 \times W \times 8 = 16W\), which matches the middle term.

Since all conditions for a perfect square trinomial are met, we can factor it as:

\[
W^2 + 16W + 64 = (W + 8)^2
\]

So, the factored form of \(W^2 + 16W + 64\) is \((W + 8)^2\).

Would you like more details or have any questions? Here are some related questions:

1. How do you factor the expression \(x^2 + 10x + 25\)?
2. Can you explain why \(a^2 - 2ab + b^2\) is factored as \((a - b)^2\)?
3. What is the difference between a perfect square trinomial and a regular trinomial?
4. How do you recognize whether a trinomial is a perfect square trinomial?
5. How would you factor the expression \(x^2 + 14x + 49\)?

**Tip:** When factoring trinomials, always check if it can be factored as a perfect square trinomial before trying other methods like grouping or using the quadratic formula.

Learn how to factor the perfect square trinomial W^2 + 16W + 64 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring perfect square trinomials using the formula (a + b)^2. Suitable for students in Grades 7-9.

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