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 = x2 − 2xy + y2 to square your number without using a calculator.

let's pick 35.

35 = 40 - 5

square both sides.

35^2 = (40 - 5)^2

now apply the square of a binomial to the right side, (x - y)^2 = x^2 - 2xy + y^2.

35^2 = (40 - 5)^2 =

= 40^2 - 2(40)(5) + 5^2

= 1600 - 400 + 25

= 1200 + 25

= 1225

35^2 = 1225

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

cheater

step-by-step explanation: