Question

question
type the correct answer in each box.
use the perfect square trinomial identity to write this expression in factored form:
x² + 10x + 25.

x² + 10x + 25 = (□ + □)²

Explanation:

Step1: Recall perfect square identity

The perfect square trinomial identity is \(a^2 + 2ab + b^2=(a + b)^2\).

Step2: Identify \(a\), \(2ab\), \(b^2\)

For \(x^2+10x + 25\), we have \(a^2=x^2\), so \(a = x\); \(b^2 = 25\), so \(b=5\) (since \(5^2 = 25\)); and \(2ab=2\times x\times5 = 10x\), which matches the middle term.

Step3: Apply the identity

Using the identity \(a^2+2ab + b^2=(a + b)^2\) with \(a=x\) and \(b = 5\), we get \(x^2+10x + 25=(x + 5)^2\).

Answer:

\(x\), \(5\) (so the expression is \((x + 5)^2\))