Question

Math question, please answer.

Answer 1

Alright, so we have

`2 (x^(2) + y^(2) )^(2) + x^(4)+y^(4))= [blank]+x^(4)+y^(4)` to fill in the first box. Since the general equation for expanding (x+y)² is x²+2xy+y², we can substitute x² for x and y² for y to get
`(x^(2) + y^(2) )^(2)=x^(4)+2x^(2)y^(2)+y^(4)`, making it


`(x^(2) + y^(2) )^(2) + x^(4)+y^(4)=x^(4)+2x^(2)y^(2)+y^(4)+ x^(4)+y^(4)`
Crossing out one x^4 and one y^4 from both sides, we're left with the blank being

`(x^(2) + y^(2) )^(2)=x^(4)+2x^(2)y^(2)+y^(4)`

For the second blank, we can make x^4+x^4=2x^4 and y^4+y^4=2y^4, resulting in

`(x^(2) + y^(2) )^(2) + x^(4)+y^(4)=x^(4)+2x^(2)y^(2)+y^(4)+ x^(4)+y^(4) =2x^(2)y^(2)+2x^(4)+2x^(4)`

Onto the last blank, we have
`2x^(2)y^(2)+2x^(4)+2x^(4)`.

We can simply factor the two - this means that we divide the whole line by 2 and multiply the quotient by 2 to have it equal the original line - to get

`2 (x^(2) + y^(2) )^(2) + x^(4)+y^(4))`

Feel free to ask further questions!