(x+y)*(x-y)

[Wictorian]

How would I calculate this?

[seon123]

Typically, one would just remember that it's x²-y²

[Excorcist_46]

(x^2)-(y^2). This is middle school maths

[Wictorian]

LOL

[DoctorNick]

x*x+y*(-y)

[Enderman]

(a+b) * (c+d)

expands to 

a*c + a*d + b*c + b*d

 

now put in the x and y (don't forget the minus sign in front of the second y) and you get

 

x*x + x*-y + y*x + y*-y

 

which is the same as

x*x - x*y + x*y - y*y

 

you can see the middle two terms cancel out and you're left with just x*x - y*y

[WkdPaul]

* thread moved to the off-topic section *

[Wictorian]

22 hours ago, wkdpaul said:

* thread moved to the off-topic section *

I thought it was already off topic

[TetraSky]

Enderman answered it well.

But going a step further, in addition to what they've said

This his how I would explain it to someone who just doesn't understand the "expand" thing of :

(a+b) * (c+d) = a*c + a*d + b*c + b*d

 

 

(x+y) * (x-y) is the equation while (a+b) * (c+d) is the basis of it

 

You need to multiply each numbers of each parenthesis, with the numbers of the other parenthesis.

And do so in order.

 

Lets start with a*c

You take the x in the first parenthesis and you multiply it with the x in the other parenthesis.

x*x

This equals x². Why x² ? Because the exponent is just a number that tells you how many times you should multiply the number it is attached to, by itself. x² = x*x

 

Now you follow up with a*d, still with the x of the first parenthesis, but this time, with the y of the second parenthesis.

x*-y

This becomes -xy

Why is it a minus? Because a positive times and negative, always result in a negative. And y in the second parenthesis is negative.

 

So now you’ve found the multiplication values of the x, or a*c + a*d

x² – xy

Alright, now lets do the same with the y, starting with b*c

 

Take the y of the first parenthesis, it’s a positive because it has a + in front a it. Multiply it with the x of the second parenthesis.

+ xy

 

Now our answer should look like this thus far :

x² – xy + xy

(this is a*c + a*d + b*c)

 

Why did I write it xy instead of yx? Simply because it’s easier this way to not get confused, but it would’ve been valid regardless.

 

And now, all that's left is b*d. We multiply the y of the first parenthesis with the y of the second parenthesis. A plus multiplied with a minus equals a minus.

 

+y * -y = -y²

 

Almost done!
Our equation is complete, it now look like this

a*c + a*d + b*c + b*d = x² – xy + xy -y²

 

Simply do the addition between -xy and +xy. They cancel each other, so think of it as -1 + 1 = 0

The result is

x² + 0 - y²

 

Get rid of the 0 because it's meaningless and you get x² - y²