Question

which of the following leading terms would make the expression a perfect square trinomial?
______ +156zy + 169y²
a 36x²
b 81x²
c 49x²
d 25x²

Explanation:

Step1: Recall perfect square trinomial formula

A perfect square trinomial is of the form \(a^{2}+2ab + b^{2}=(a + b)^{2}\) or \(a^{2}-2ab + b^{2}=(a - b)^{2}\). In the given expression \(\_\_\_+156zy + 169y^{2}\), we can consider \(b^{2}=169y^{2}\), so \(b = 13y\) (since \(13^{2}=169\)). Also, \(2ab=156zy\).

Step2: Solve for \(a\)

We know that \(2ab = 156zy\) and \(b = 13y\). Substitute \(b\) into the equation:
\(2a(13y)=156zy\)
Simplify the left - hand side: \(26ay = 156zy\)
Divide both sides by \(26y\) (assuming \(y
eq0\)): \(a=\frac{156zy}{26y}=6z\)? Wait, no, wait. Wait, the variable here is \(x\) and \(y\)? Wait, maybe it's a typo, maybe the middle term is \(156xy\) (since the options are in terms of \(x^{2}\)). Let's correct that. Let's assume the middle term is \(156xy\) (maybe a typo with \(z\) and \(x\)). Then, \(b^{2}=169y^{2}\), so \(b = 13y\), and \(2ab = 156xy\). Then:
\(2a\times13y=156xy\)
\(26ay=156xy\)
Divide both sides by \(26y\): \(a = 6x\). Then \(a^{2}=(6x)^{2}=36x^{2}\).

Answer:

A. \(36x^{2}\)