a) Find a method to compute ac,ad+bc and bd using three multiplications,given reals a,b,c and d.(Note that since (ax +b) *(cx+d) = acx² +(ad+bc)x +bd ,this result allows us to multiply two degree-one polynomials using three real multiplications.)

b)Develop a divide and conquer algorithm for multiplying two degree-n polynomials

A(x)= a_nxⁿ + a_n-1x^n-1+........+a₁x +a₀

and

B(x)=b_nxⁿ+ b_n-1x^n-1+........+b₁x + b₀ in O (n ^log₂3) time and prove the running time by writing and analyzing a recurrence relation.You may assume that n is a power of 2.Your algorithm takes as input coefficients a_n,...............,a₀,b_n,............,b₀ and outputs the coefficient c_2n,,c_2n-1,......c₀ of polynomial c(x)=A(x)B(x).

HINT: One approach is to divide the coefficients into upper-half and lower half based on their indices and apply the result in the previous subproblem.