Question

this is the only question in this section.
question
factor.
$x^2 + 14x + 49$
answer attempt 1 out of 10

Explanation:

Step1: Recall the perfect square trinomial formula

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

Step2: Identify \(a\) and \(b\) in the given expression

For the expression \(x^2+14x + 49\), we have \(a = x\) (since \(x^2=a^2\)), and \(2ab=14x\). Substituting \(a = x\) into \(2ab = 14x\), we get \(2\times x\times b=14x\), which simplifies to \(2b = 14\), so \(b = 7\). Also, \(b^2=7^2 = 49\), which matches the constant term in the given expression.

Step3: Apply the perfect square trinomial formula

Using the formula \(a^2+2ab + b^2=(a + b)^2\) with \(a=x\) and \(b = 7\), we get \(x^2+14x + 49=(x + 7)^2\).

Answer:

\((x + 7)^2\)