Question

Which shows a perfect square trinomial? A 50 y squared minus 4 x squared B 100 minus 36 x squared y squared C 16 x squared + 24 x y + 9 y squared D 49 x squared minus 70 x y + 10 y squared

Answer 1

The Correct Answer is Option C

Answer 2

Answer: OPTION C

Explanation:

For this problem it is important to remember that a trinomial is a polynomial with three terms and a binomial is a polynomial with two terms.

By definition, when you square a binomial, you get a perfect square trinomial:

`(a \± b)^2=a^2 \± 2ab + b^2`

Observe the trinomial given in Option C:

`16 x^2 + 24 x y + 9 y^2`

You can identify that:

`a^2=16x^2\\a=√(16x^2)=4x\\\\\\b^2=9y^2\\b=√(9y^2)=3y\\\\\\2ab=2(4x)(3y)=24xy`

Therefore, you can conclude that
`16 x^2 + 24 x y + 9 y^2` is a perfect square trinomial.