Prove this is never positive

[Student31]

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

So far, I have got:

(x+1)(x+7) = x²+8x+7
3(x²+8x+7)=3x²+24x+21
(2x+5)²=(2x+5)(2x+5)= 4x²+20x+25
(3x²+24x+21)-(4x+20x+25)=x²-4x-4
-x²-4x-4=-1(x²+4x+4)=-1((x+2)(x+2))
Because it will always be multiplied by -1, it is never positive

This is out of 5 marks but I only got 4 marks. I don't know where the remaining mark is........

 

[yoscar04]

There is a small typo in (3x²+24x+21)-(4x+20x+25)=x²-4x-4. It should be (3x²+24x+21)-(4x²+20x+25) =-x²+4x-4=-(x-2)². So the correct final expression should be -(x-2)² which is always non positive. So what is missing?

 

[Student31]

Thank you yoscar04 this helped

 

[Steven G]

(3x²+24x+21)-(4x+20x+25)=x²-4x-4

You have x instead of x². I assume that was a typo.

The real problem is that you did three subtractions and got two wrong.

3-4 = 1 is not correct.
24-20 = -4 is not correct.
21-25 = -4 is correct.