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.

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

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: