Basic Trinomial Check requested

[elron]

I've run in to a trinomial in a math tutorial. I feel quite stupid over this because I know how to do the math, but I can't get the answer the tutorial is offering. I've double checked the tutorials answer with a online trinomial calculator and it appears to be correct. If any one could take a quick peek at this it would be greatly appreciated.

Here is the trinomial I'm trying to solve, It's in the context of a Integral volume equation(http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithRings.aspx)

(x^2 - 4x +5)^2
The answer the tutorial has is this:
x^4 -8^3 + 26x^2 - 40x + 25

My first step produces:
x^4 - 4x^3 + 5x^2 - 4x^3 - 8x^2 - 20x + 5x^2 - 20x +25

Combining terms with like degrees I get:
x^4 - 8x^3 + 2x^2 - 40x + 25

Obviously I'm getting the 2x^2 wrong. I've done this problem five times now and am not getting it.

Any help would be a relief. Thank you in advanced.

 

[Jason76]

Hi, do you see the logic here?

\(\displaystyle (x^2 - 4x +5)^2\)

\(\displaystyle (x^2 - 4x +5)(x^2 - 4x +5)\)

\(\displaystyle x^{4} - 4x^{3} + 5x^{2} - 4x^{3} + 16x^{2} - 20x + 5x^{2} - 20x + 25\)

\(\displaystyle x^{4} -8x^{3} + 26x^{2} - 40x + 25\)

 

[stapel]

(x^2 - 4x +5)^2
The answer the tutorial has is this:
x^4 -8^3 + 26x^2 - 40x + 25

My first step produces:
x^4 - 4x^3 + 5x^2 - 4x^3 - 8x^2 - 20x + 5x^2 - 20x +25

The squared terms are formed by the products (x^2)(+5) (twice) and (-4x)(-4x).

What is the value of (-4)(-4)?

 

[Bob Brown MSEE]

Hi, do you see the logic here?

\(\displaystyle (x^2 - 4x +5)^2\)

\(\displaystyle (x^2 - 4x +5)(x^2 - 4x +5)\)

\(\displaystyle (x^2(x^2 - 4x +5) - 4x(x^2 - 4x +5) +5(x^2 - 4x +5))\) <============

\(\displaystyle x^{4} - 4x^{3} + 5x^{2} - 4x^{3} + 16x^{2} - 20x + 5x^{2} - 20x + 25\)

\(\displaystyle x^{4} -8x^{3} + 26x^{2} - 40x + 25\)

One more step inserted above

 

[elron]

Boy I feel dumb.

OK, I was adding instead of multiplying to spite the fact that I knew what I was doing. I seem to have reworked in my brain that 4*4 is 8. I need to do math when my mind is sharper. Thank you all for pointing this silly mistake out. 3am practice problems aren't the best idea.

 

[HallsofIvy]

Even late in the morning, I'm no good until after my second or third cup of coffee!