Subtracting Polynomials.

[WTF?]

I have this problem, that I'm confused about or insecure.

Expand and Simplify

\(\displaystyle (2x +1)^2 - (2x -5)^2\)

I got \(\displaystyle 14x+26\)

Is this incorrect?

Thanks.

 

[Unco]

\(\displaystyle \L -(2x \, - \, 5)^2 = -(4x^2 \, - \, 20x \, + \, 25)\)

• (not -10x)

Also be careful to subtract each term in the paratheses.

 

[WTF?]

\(\displaystyle \L -(2x \, - \, 5)^2 = -(4x^2 \, - \, 20x \, + \, 25)\)

• (not -10x)

Also be careful to subtract each term in the paratheses.

Wait, you're making it confusing :?

Wouldn't I first expand the first term?
\(\displaystyle (2x+1)^2\) becomes \(\displaystyle (2x+1)(2x+1)\) thus \(\displaystyle (4x^2 +4x +1)\)

Second term, \(\displaystyle (2x-5)^2\) becomes \(\displaystyle (2x-5)(2x-5)\) thus \(\displaystyle (4x^2 -20x +25)\)

So...
\(\displaystyle (4x^2 +4x +1)-(4x^2 -20x +25)\)

Then I just subtract as per usual...then the \(\displaystyle 4x^2\) cancels out, and then \(\displaystyle 4x-(-20x)\) is \(\displaystyle 14x\) so then \(\displaystyle 1-(+25)\) is \(\displaystyle 26\) and etc.?

 

[Unco]

I tried (evidently pretty poorly) to guess your error. I got it in my last sentence though!

-(-20x) = +20x

-(+25) = -25

 

[WTF?]

I tried (evidently pretty poorly) to guess your error. I got it in my last sentence though!

-(-20x) = +20x

-(+25) = -25

So am I wrong or what dude, you lost me.

 

[Unco]

4x - (-20x) = 4x + 20x = 24x

and

1 - (+25) = 1 - 25 = -24

Have I found you?

 

[Mrspi]

\(\displaystyle \L -(2x \, - \, 5)^2 = -(4x^2 \, - \, 20x \, + \, 25)\)

• (not -10x)

Also be careful to subtract each term in the paratheses.

Wait, you're making it confusing :?

Wouldn't I first expand the first term?
\(\displaystyle (2x+1)^2\) becomes \(\displaystyle (2x+1)(2x+1)\) thus \(\displaystyle (4x^2 +4x +1)\)

Second term, \(\displaystyle (2x-5)^2\) becomes \(\displaystyle (2x-5)(2x-5)\) thus \(\displaystyle (4x^2 -20x +25)\)

So...
\(\displaystyle (4x^2 +4x +1)-(4x^2 -20x +25)\)

Then I just subtract as per usual...then the \(\displaystyle 4x^2\) cancels out, and then \(\displaystyle 4x-(-20x)\) is \(\displaystyle 14x\) so then \(\displaystyle 1-(+25)\) is \(\displaystyle 26\) and etc.?

You have done GREAT so far:
(4x^2 + 4x + 1) - (4x^2 - 20x + 25)

Remember that in algebra (or in arithmetic, for that matter), subtracting is the same as adding the opposite:
(4x^2 + 4x + 1) - (4x^2 - 20x + 25)
is the same as
(4x^2 + 4x + 1) + (-)(4x^2 - 20x + 25)
(4x^2 + 4x + 1) + (-4x^2 + 20x - 25)
4x^2 + 4x + 1 - 4x^2 + 20x - 25
24x - 24

Looks like you made a simple arithmetic mistake.

 

[WTF?]

\(\displaystyle \L -(2x \, - \, 5)^2 = -(4x^2 \, - \, 20x \, + \, 25)\)

• (not -10x)

Also be careful to subtract each term in the paratheses.

Wait, you're making it confusing :?

Wouldn't I first expand the first term?
\(\displaystyle (2x+1)^2\) becomes \(\displaystyle (2x+1)(2x+1)\) thus \(\displaystyle (4x^2 +4x +1)\)

Second term, \(\displaystyle (2x-5)^2\) becomes \(\displaystyle (2x-5)(2x-5)\) thus \(\displaystyle (4x^2 -20x +25)\)

So...
\(\displaystyle (4x^2 +4x +1)-(4x^2 -20x +25)\)

Then I just subtract as per usual...then the \(\displaystyle 4x^2\) cancels out, and then \(\displaystyle 4x-(-20x)\) is \(\displaystyle 14x\) so then \(\displaystyle 1-(+25)\) is \(\displaystyle 26\) and etc.?

You have done GREAT so far:
(4x^2 + 4x + 1) - (4x^2 - 20x + 25)

Remember that in algebra (or in arithmetic, for that matter), subtracting is the same as adding the opposite:
(4x^2 + 4x + 1) - (4x^2 - 20x + 25)
is the same as
(4x^2 + 4x + 1) + (-)(4x^2 - 20x + 25)
(4x^2 + 4x + 1) + (-4x^2 + 20x - 25)
4x^2 + 4x + 1 - 4x^2 + 20x - 25
24x - 24

Looks like you made a simple arithmetic mistake.

Ah, I see. So the - by the parentheses multiplies the others by -1.

 

[Gene]

I do wish everyone would stop quoting entire posts. It becomes difficult to tell where one ends and an addition begins. One or two lines from it is almost always enough. And quoting a quote of a quote???? Ughhh!
--------------------
Gene

 

[thesloc]

[quote="WTF?":1t3g2v1s]

\(\displaystyle \L -(2x \, - \, 5)^2 = -(4x^2 \, - \, 20x \, + \, 25)\)

• (not -10x)

Also be careful to subtract each term in the paratheses.

Wait, you're making it confusing :?

Wouldn't I first expand the first term?
\(\displaystyle (2x+1)^2\) becomes \(\displaystyle (2x+1)(2x+1)\) thus \(\displaystyle (4x^2 +4x +1)\)

Second term, \(\displaystyle (2x-5)^2\) becomes \(\displaystyle (2x-5)(2x-5)\) thus \(\displaystyle (4x^2 -20x +25)\)

So...
\(\displaystyle (4x^2 +4x +1)-(4x^2 -20x +25)\)

Then I just subtract as per usual...then the \(\displaystyle 4x^2\) cancels out, and then \(\displaystyle 4x-(-20x)\) is \(\displaystyle 14x\) so then \(\displaystyle 1-(+25)\) is \(\displaystyle 26\) and etc.?

You have done GREAT so far:
(4x^2 + 4x + 1) - (4x^2 - 20x + 25)

Remember that in algebra (or in arithmetic, for that matter), subtracting is the same as adding the opposite:
(4x^2 + 4x + 1) - (4x^2 - 20x + 25)
is the same as
(4x^2 + 4x + 1) + (-)(4x^2 - 20x + 25)
(4x^2 + 4x + 1) + (-4x^2 + 20x - 25)
4x^2 + 4x + 1 - 4x^2 + 20x - 25
24x - 24

Looks like you made a simple arithmetic mistake.

Ah, I see. So the - by the parentheses multiplies the others by -1.[/quote:1t3g2v1s]
You're correct.

 

[Gene]

Yes, like that one by Thesloc. Two pages for ONE line. Arghhhh!!!!