Answer:
The value of q that makes the expression a perfect square is q = 4.
Step-by-step explanation:
Perfect square:
A perfect square expression has the following format:
[tex](a - b)^2 = a^2 - 2ab + b^2[/tex]
In this question:
[tex]9x^2 - 12x + q[/tex] is a perfect square, we have to find the value of q.
First we have to find the value of a, looking at the equivalent formula above. So
[tex]a^2 = 9x^2[/tex]
[tex]a = \sqrt{9x^2}[/tex]
[tex]a = 3x[/tex]
Since the second term, which is -2ab, is -12x, we have that:
[tex]-2ab = -12x[/tex]
[tex]-2(3x)b = -12x[/tex]
[tex]-6xb = -12x[/tex]
[tex]6b = 12[/tex]
[tex]b = \frac{12}{6}[/tex]
[tex]b = 2[/tex]
q is b squared. So
[tex]q = b^2 = 2^2 = 4[/tex]
The value of q that makes the expression a perfect square is q = 4.
