SOLUTION: What do you get as an answer when you multiply(x^2+y^2)(x^2+y^2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What do you get as an answer when you multiply(x^2+y^2)(x^2+y^2)      Log On


   

Question 193778: What do you get as an answer when you multiply(x^2+y^2)(x^2+y^2)
Found 2 solutions by checkley77, jim_thompson5910:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(x^2+y^2)
(x^2+y^2)
----------------
x^4+x^2y^2+x^2y^2+y^4
x^4+2x^2y^2+y^4

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2%2By%5E2%29%28x%5E2%2By%5E2%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%28x%5E2%29%2By%5E2%29%28highlight%28x%5E2%29%2By%5E2%29 Multiply the First terms:%28x%5E2%29%2A%28x%5E2%29=x%5E4.


%28highlight%28x%5E2%29%2By%5E2%29%28x%5E2%2Bhighlight%28y%5E2%29%29 Multiply the Outer terms:%28x%5E2%29%2A%28y%5E2%29=x%5E2%2Ay%5E2.


%28x%5E2%2Bhighlight%28y%5E2%29%29%28highlight%28x%5E2%29%2By%5E2%29 Multiply the Inner terms:%28y%5E2%29%2A%28x%5E2%29=x%5E2%2Ay%5E2.


%28x%5E2%2Bhighlight%28y%5E2%29%29%28x%5E2%2Bhighlight%28y%5E2%29%29 Multiply the Last terms:%28y%5E2%29%2A%28y%5E2%29=y%5E4.


---------------------------------------------------
So we have the terms: x%5E4, x%5E2%2Ay%5E2, x%5E2%2Ay%5E2, and y%5E4


x%5E4%2Bx%5E2%2Ay%5E2%2Bx%5E2%2Ay%5E2%2By%5E4 Now add every term listed above to make a single expression.


x%5E4%2B2%2Ax%5E2%2Ay%5E2%2By%5E4 Now combine like terms.


So %28x%5E2%2By%5E2%29%28x%5E2%2By%5E2%29 FOILs to x%5E4%2B2%2Ax%5E2%2Ay%5E2%2By%5E4.


In other words, %28x%5E2%2By%5E2%29%28x%5E2%2By%5E2%29=x%5E4%2B2%2Ax%5E2%2Ay%5E2%2By%5E4.