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Prove 3(x+1)(x+7)-(2x+5)² is never positive

So,
3(x+1)(x+7)-(2x+5)(2x+5)
=3(x²+8x+7)-(4x²+20x+25)
=3x²+24x+21-4x²-20x-25
=-x²+4x-4

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8 answers

  1. = -(x^2-4x+4)
    = -(x-2)^2

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  2. Hi, you information was really useful but for some reason I only got 4 marks out of 5 on mathswatch, do you know why?

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  3. 3(x + 1)(x + 7) - (2x + 5)(2x + 5)
    = 3(x² + 8x + 7)- (4x²+ 20x + 25)
    = 3x² + 24x + 21- 4x²- 20x- 25
    = -x² + 4x - 4
    = -1(x - 2)²
    A squared number is always positive, but when you multiply it with a negative number, it is always negative, never positive.

    ^This will give you all 5 marks on Mathswatch. Hope it helps :)

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  4. Sorry It actually did

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  5. this was extremely useful. thank you

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  6. THANK YOU SM

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  7. I don't know what you mean by it "didn't work." It just shows that the expression is never positive.

    (x-2)^2 is a square, so it is always positive

    So, -(x-2)^2 is never positive.

    Trying to plug a formula into a request for a proof will never work. The logic is what counts.

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  8. The answer above didn't work

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