ANSWER
[tex]{(3a + 4b)}^{2} [/tex]
EXPLANATION
The given function is:
[tex] 9{a}^{2} + 24ab + 16 {b}^{2} [/tex]
This can be rewritten as
[tex]{(3a)}^{2} + 2(3 \times 4)ab + {(4b)}^{2} [/tex]
Recall that:
[tex] {x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2} [/tex]
Let x=3a and y=4b,
Then,
[tex]{(3a)}^{2} + 2(3 \times 4)ab + {(4b)}^{2} = {(3a + 4b)}^{2} [/tex]
Hence the fully factored form is:
[tex]{(3a + 4b)}^{2} [/tex]
