;; a is a polynomial and b is a polynomial (list of terms)
;; poly+term* can add poly+terms

(define (poly+poly* a b temp) (if (null? b) temp (poly+poly* (poly+term* a (car b)) (cdr

b) (poly+term* a (carb))))))

;;returns a+b

;;multiplies a polynomial by a term

(define (poly-term* t a temp) (if (null? a) temp (poly-term* t (cdr a) (map (lambda (x)

((make-term (x) (+ (pow-of x) (pow-of (car a))) (* (coef-of x) (coef-of (car a)))))

a))))

;; foil out a and b using poly-term*
;; returns a list of lists

(define (foil* a b temp) (if (null? a) temp (foil* (poly-term* (cdr a) b) cons(

(poly-term* (car a) b) temp))))


;;simplify foil

(define (foil** a b) (foil* a b '()))

;;now to simplify polynomial using poly+poly*

(define (simplify lst temp) (if (null? (car (car lst))) temp (simplify (cdr lst) cons(

(poly+poly* (car lst) (car (cdr lst)) '()) '())))

;; now multiply will return a*b simplified

(define (multiply a b) (simplify (foil** a b) '()))