Question

factor $144x^{2}+288x + 144$ using the perfect square trinomial method (if applicable).
a. $(12x + 12)^{2}$
b. not a perfect square trinomial
c. $12x(x + 24)$
d. $(12x - 12)^{2}$

Explanation:

Step1: Identify $a^2$ term

$144x^2=(12x)^2$, so $a=12x$

Step2: Identify $b^2$ term

$144=12^2$, so $b=12$

Step3: Verify middle term

Check $2ab=2\times12x\times12=288x$, matches given term

Step4: Write perfect square form

$(a+b)^2=(12x+12)^2$

Answer:

a. $(12x + 12)^2$