To factor 9x^2 + 24x + 16, we can use the factoring by grouping method.
First, we can find two numbers that multiply to give 9*16=144 and add to give 24. These numbers are 12 and 12.
Next, we can split the middle term 24x into two terms by using these numbers:
9x^2 + 12x + 12x + 16
Now, we can factor out the GCF from the first two terms and the last two terms:
3x(3x + 4) + 4(3x + 4)
Notice that the terms inside the parentheses are the same. We can factor out the common factor (3x+4) from both terms:
(3x+4)(3x+4)
or we can write it in the simplified form:
(3x+4)^2
Therefore, 9x^2 + 24x + 16 can be factored as (3x+4)^2.