Question

1. $121n^2 + 154n + 49$

Explanation:

Step1: Identify perfect squares

Notice that \(121n^2=(11n)^2\) and \(49 = 7^2\).

Step2: Check middle term

The middle term should be \(2\times11n\times7 = 154n\), which matches the given middle term.

Step3: Apply perfect square formula

The perfect square trinomial formula is \(a^2 + 2ab + b^2=(a + b)^2\). Here, \(a = 11n\) and \(b = 7\), so \(121n^2+154n + 49=(11n + 7)^2\).

Answer:

\((11n + 7)^2\)