Question

Task 2 Polynomial Identities Part 1. Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)^2 = x^2 − 2xy + y^2 to square your number without using a calculator. Part 2. Choose two values, a and b, each between 8 and 15. Show how to use the identity a^3 + b^3 = (a + b)(a^2 − ab + b^2) to calculate the sum of the cubes of your numbers without using a calculator.

Answer 1

Answer:

see below

Step-by-step explanation:

49

50-1

We want to find 49^ 2 using the following identity

(x − y)^2 = x^2 − 2xy + y^2

Let x= 50 and y=1

(50-1) ^2 = 50^2 - 2 *50 *1 + 1^2

49^2 = 2500 - 100 +1

        = 2400 +1

        = 2401

a = 10   b= 13

a^3 + b^3 = (a + b)(a^2 − ab + b^2)

10^3 + 13^3  = ( 10+13) ( 10^2 - 10*13 + 13^2)

                     = (23) ( 100-130+169)

                      = 23 ( 139)

                       =3197