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Another maths qu? ?

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when Y is odd, explain why (y+5)(y-1) is an even number.

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  1. (y+5)(y-1)

    =y^2-y+5y-5

    y^2+4y-5

    the square of odd number is an odd number, also any odd number multiplied by 4 would give an even number . so if you inpu 3 instead of y

    you will get

    3^2+4(3)-5

    9+12-5

    16


  2. u have to times the 2 brackets to gether eg: y=3

    (3+5)(3-1)

    8x3= 24

  3. If you add two odd numbers, their sum is even so y+5 is even.

    If you subtract two odd numbers, their difference is even so y-1 is even.

    When you multiply two even numbers, their product is even so

    (y+5)(y-1) is even.

  4. Adding or subtracting on odd number from another odd number will always give you an even number. Pick any odd number for y, subtracting 1 or adding 5 will always give you an even number, and multiplying two even numbers will always give you an even number.

    ex. y= 7

    (7+5)(7-1)= (12) (6)= 84

    ex. y= 15

    (15+5) (15-1)= (20)(14)= 280

  5. when y is odd so sum of 2 odds is even

    so y+5=even

    substraction of 2 odds is also even.

    y-1 = even

    so we have (even)*(even)  =(y+5) (y-1)

    multiplication of 2 even numbers is always even


  6. If y is odd, it can be expressed as 2n + 1 for some integer n, regardless of whether n is odd or even.

    (y+5)(y-1) = (2n+1+5)(2n+1-1) = (2n+6)(2n) = 2 (2n^2 + 6n) is a multiple of 2 so is even.
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