Name: Date:

Question 1: Prove that the difference of the squares of 2 consecutive odd numbers is always divisible by 8 |

Question 2: Prove that (5n+8)^2 -(5n-8)^2 is always a multiple of 5 |

Question 3: Prove the identity (n+2)^2 -(2n+12) ≡ (n+4)(n-2) |

Question 4: Prove that the sum of 3 consecutive numbers is always a multiple of 3 |

© GCSEMathsWorksheets.com

Show Answers
Hide Answers

© GCSEMathsWorksheets.com

# Answers

Question 1: (2n+3)^2-(2n+1)^2 =4n^2+12n+9-(4n^2+4n+1) =8n+8=8(n+1) therefore the difference of the squares of 2 consecutive odd numbers is always divisible by 8 |

Question 2: (5n+8)^2 -(5n-8)^2 =(25n^2+80n +64)-(25n^2-80n +64) =160n=5 \times 32n Therefore (5n+8)^2 -(5n-8)^2 is a multiple of 5 |

Question 3: (n+2)^2 -(2n+12) =(n^2+4n +4)-(2n+12) =n^2+2n-8 =(n+4)(n-2) |

Question 4: n+(n+1)+(n+2) =3n+3 =3(n+1) Therefore the sum of 3 consecutive numbers is always a multiple of 3 |