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

Answer: OPTION C

Step-by-step 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:

 $a^2=16x^2\\a=\sqrt{16x^2}=4x\\\\\\b^2=9y^2\\b=\sqrt{9y^2}=3y\\\\\\2ab=2(4x)(3y)=24xy$

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

Answer 2

The Correct Answer is Option C