Question 984500
younger=x
older=38-x
;
34-x=(x-4)^2
34-x=x^2-8x+16
0=x^2-7x-18
(x-9)(x+2)=0
x=9; ignore x=-2

The ages are 9 and 29, the product (answer) is 261.

Four years ago, the ages were 5 and 25.  Check.