You have been hired as an efficiency expert for math nerds inc. the company wants to cut costs and increase profits by increasing the number of math problems their employees can solve in a day. your job is to the math nerds employees solve math problems more quickly. show the math nerds employees how to rework each problem below using a polynomial identity. (x2+y2)2=(x2-y2)2+(2xy)2
show the math nerds employees how much time you save on each problem by using the polynomial identity to simplify.
1) ( x+2 ) 2 (x+2) 2 = (x+y) 2 =x 2 +2xy+ y 2
2) ( x−3 ) 3 (x−3) 3 = (x−y) 3 =x 3 −3 x 2 y+3x y 2 − y 3

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?