What is (x+y)(x-y)?

Answer 1

x^2-2xy-y^2 = (x+y)(x-y)

Answer 2

It's a simple answer, just make sure you approach it properly. You may have heard of FOIL, or maybe not. Regardless, if anyone ever tells you to use it, don't. The best way to go about this is to understand how to multiply polynomials. When you multiply two polynomials, you must multiply each term in the first with each term in the second:

(x+y)(x-y)

Now, the easiest way to do this is methodical: start at the first term of the first binomial. Multiply it with each term of the second binomial. So we'll multiply the x in the first and the x in the second. Then the x in the first and the -y in the second.

(x+y)(x-y) = x*x + x*(-y)

Once we've gone through all the terms in the second, we'll move onto the next term in the first, and do the same process. We'll start with y of the first binomial and multiply it with x of the second binomial, then -y of the second binomial:

(x+y)(x-y) = x*x + x*(-y) + y*x + y*(-y)

Now we simplify:

(x+y)(x-y) = x^2 - xy + xy - y^2
(x+y)(x-y) = x^2 - y^2 [because -xy+xy = 0]

And you're done. The reason you never use FOIL is because it only works for two binomials (FOIL stands for first, outside, inside, last). For anything larger than two terms, FOIL is completely useless, so get in the habit of doing it the way above.

Hope this helps.

"FOIL killed my inner child."

Answer 3

(x+y)(x-y)=

filling in some blanks that matematicians remove because they are lazy and then it actually stands

(+x+y)*(+x-y)

Then you take the first letter (+x) and multiply with the second ().

+x*+x and +x*-y.

Then you take the second letter (+y) and multiply with the second ().
+y*+x and +y*-y.

So if we add these we get x^2-xy+xy-y^2.

The xy cancels eachother out, leaving you with
x^2-y^2.

This is called the conjugat rule or similar and you should try to learn the way it works. Try replacing the letters with numbers and see how it works out.

(Ps - the ^2 means square ie that you write a small 2 just right of the letter).

Answer 4

x^2 - y^2

Answer 5

That would be x (squared)plus y (squared) because if you FOIL it, (first, outside inside last) you get x (squared) minus xy plus xy plus y (squared) and the middle two terms cancel out, so your answer is simply x squared + y squared.

Answer 6

x^2 - y^2

its the difference of squares formula

Answer 7

Use the distributive rule:

(x+y)(x-y) = ( (x+y)*x - (x+y)*y )

=(x*x + y*x) - (x*y + y*y)
=(x^2 + yx - xy - y^2) ----> "yx" is the same as "xy", so combine them:

(x^2 + 0 - y^2)
=x^2 - y^2

Answer 8

(x+y)(x-y)
= x^2 + xy - xy - y^2
= x^2 - y^2 (difference of 2 squares)

Answer 9

foil - FIRST ... OUTSIDE ... INSIDE .. LAST
+X^2 -XY +XY -Y^2
INSIDE TERMS CANCEL
LEAVING X^2 - Y^2

Answer 10

x square - y square