If a = 4 and b = 5, what is the value of a^2 + b^2?

To find the value of ( a^2 + b^2 ) when ( a = 4 ) and ( b = 5 ), start by calculating ( a^2 ) and ( b^2 ).

First, compute ( a^2 ):

[

a^2 = 4^2 = 16

]

Next, compute ( b^2 ):

[

b^2 = 5^2 = 25

]

Now, add these two results together:

[

a^2 + b^2 = 16 + 25 = 41

]

Therefore, the correct value of ( a^2 + b^2 ) when ( a = 4 ) and ( b = 5 ) is 41. This shows that the calculations were done correctly based on the equations for squaring each variable and then summing them up.