Question

Which polynomial is a perfect square trinomial?

25x2 − 20x − 16


9a2 − 30a − 25


25b2 − 15b + 9


16x2 − 24x + 9

Answer 1

`\large\boxed{16x^2-24x+9=(4x-3)^2}`

Explanation:

`\text{Perfect square:}\ (a-b)^2=a^2-2ab+b^2\\=======================\\\\25x^2-20x-16\to\text{NOT. Because is}\ -16=-4^2\\\\9a^2-30a-25\to\text{NOT. Because is}\ -25=-5^2\\\\25b^2-15b+9=(5b)^2-2(5b)\left((3)/(2)\right)+3^2\to\text{NOT. Because is}\ b=(3)/(2)\ \text{and}\ b^2=3^2\\\\16x^2-24x+9=(4x)^2-2(4x)(3)+3^2=(4x-3)^2\ \boxed{YES\ :)}`