Question

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 help 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

Answer 1

So in order to find
(x+2)2
without writing (x+2)(x+2)=x2+2x+2x+4=x2+4x+4 instead say y=2 and use the identity to get
x2+2×2x+2^2=x2+4x+4