Question

Which of the following is a perfect square trinomial?

Answer 1

Answer:

A.

Step-by-step explanation:

Take a look at what happens when squaring either of these...

$(ax-by)^2=(ax-by)(ax-by)=a^2x^2-2abxy+b^2y^2\\\\(ax+by)^2=(ax+by)(ax+by)=a^2x^2+2abxy+b^2y^2$

Notice a couple of patterns.

1.  The last term has a positive coefficient.  That rules out answer choices C and D.

2.  The coefficient of the middle term is either $+2ab \text{ or } -2ab$ .  So what are a  and b?  a is the square root of the x^2 term and b is the square root of the y^2 term.

$25x^2 \Rightarrow a=5\\\\9y^2 \Rightarrow b=3\\\\ab=15\\\\2ab=30$

The middle coefficient needs to be either +30 or -30.  The answer is choice A.