P $4.[3$ pts$]($BONUS$)$ Describe a divide and conquer algorithm to compute the square

of an $n-$digit integer in $O(n^{lo{g}_{3}5})$ time, by reducing to the squaring of five $|$~$\frac{n}{3}$~$|-$digit

integers. To simplify the analysis, we assume that the numbers in the recursive calls

do not require more bits than the terms that make up these numbers. This means that

the number of digits of the integers passed to the recursive calls do not exceed $|$~$\frac{n}{3}$~$|$

Include the same points in your submission as for Problem P $2..$ Is this algorithm

asymptotically faster that your algorithm from $P2.?$

Hint: investigate the expression $(x+y+z{)}^2+(x-y+z{)}^2.$