Ask questions and get helpful answers.
Ask a New Question
  1. Questions
  2. algebra

Prove by mathematical induction that x^2n - y^2n has a factor of x+y.

My answer is incomplete since i do not know what to do next. here it is:

i.) for n=1

x^2(1) - y^2(1) = x^2 - y^2
= (x+y)(x-y)

ii.) Assume that the proposition is true for all n=k, that is, x^2k - y^2k has a factor of x+y for all k¡Ý1.

iii.) n=k+1

x^2(k+1) - y^2(k+1)
=x^2k+2 - y^2k+2
=x^2k ¡ñ x^2 - y^2k ¡ñ y^2
=(tthis part I don't know)

I hope you can help me. Thanks!

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
Kenneth

Answer this Question

Similar Questions

  1. Algebra

    Use the Factor Theorem to determine whether x+2 is a factor of P(x)=2x^4+x^3-3x-9. Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor. P(__)= x+2 is or is not a factor of P(x)____

  2. Mathematics

    Prove the following by mathematical induction for all integers (n>or=1) 1^3+2^3+3^3+-----+n^3=(n(n+1)/2)^2

  3. Astronomy

    Imagine that you have found an object out in space. When you use the inverse square law to compute its luminosity, you get a ridiculously large value. You therefore suspect that relativistic beaming is at work - the radiation is coming from a jet traveling

  4. math

    Use mathematical induction to prove that for all integers n ≥ 5, 1 + 4n < 2n

  5. math

    1. Consider the function f(x) = x3 + 7x2 + 2x - 40 . a. Find the possible rational roots of f(x) = 0. b. Use synthetic division to divide f(x) by x - 2. Show all your work. Use your answer to explain whether or not x – 2 is a factor of f(x). c. Factor

  6. E.L.A

    DO I HAVE THE RIGHT ANSWERS? What is a sound argument?(1 point) A sound argument is a loud statement. A sound argument is sensible and valid. -My answer A sound argument is impractical and hard to prove. A sound argument is a popular opinion. Which

  7. science help

    Two factors which cause global climate change are listed below. Factor 1: Volcanic eruptions. Factor 2: Changes in the amount of Sun’s heat received by the Earth’s atmosphere and surface. Which of these statements is correct about the two factors which

  8. module 8 test

    Apply the distributive property to factor out the greatest common factor. 4+10=

  9. Math

    Use Mathematical Induction to show that the statement 2 + 6 + 10 + . . . + (4n – 2) = 2n^2 is true

  10. Mathematical induction. I'm stuck. So far I have..

    For all integers n ≥ 1, prove the following statement using mathematical induction. 1+2^1 +2^2 +...+2^n = 2^(n+1) −1 Here's what I have so far 1. Prove the base step let n=1 2^1=2^(1+1)-1 False. Someone else suggested that the base step is :

Still need help?

You can ask a new question or browse existing questions.