If \( a = 4 \) and \( b = 3 \), what is \( a^2 + b^2 \)?

To determine the value of ( a^2 + b^2 ) when ( a = 4 ) and ( b = 3 ), we first compute ( a^2 ) and ( b^2 ) individually.

Calculating ( a^2 ):

[

a^2 = 4^2 = 16

]

Next, we calculate ( b^2 ):

[

b^2 = 3^2 = 9

]

Now, we add these two results together:

[

a^2 + b^2 = 16 + 9 = 25

]

Thus, the value of ( a^2 + b^2 ) is 25. This confirms that the correct answer is 25, which corresponds to one of the given choices. The other options do not align with the calculations performed, as they represent different sums that do not properly account for the squares of 4 and 3. Therefore, 25 is indeed the correct sum of the squares of ( a ) and ( b ).