Question

Which of the following is a perfect square trinomial?

Answer 1

A.

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.