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Question 1: Prove that (4n+8)^2 +(4n-8)^2 is always even |

Question 2: Prove the identity (n-4)^2 -(7n-40) ≡ (n-8)(n-7) |

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

Question 4: Prove that the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers |

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Question 1: (4n+8)^2 +(4n-8)^2 =(16n^2+64n +64)+(16n^2-64n +64) =32n^2+128=2(16n^2+64) (4n+8)^2 +(4n-8)^2 is a multiple of 2, therefore it is even |

Question 2: (n-4)^2 -(7n-40) =(n^2-8n +16)-(7n-40) =n^2-15n+56 =(n-8)(n-7) |

Question 3: n+(n+1)+(n+2)+(n+3) =4n+6 =2(2n+3) Any multiple of 2 is always even, therefore the sum of 4 consecutive numbers is always even |

Question 4: (2n+1)^2-(2n)^2 =4n^2+4n+1-4n^2 =4n+1=(2n+1)+(2n) therefore the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers |