Question

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

Answer 1

First, you want to expand the equation so it'll be: x^2+2yx+y^2=x*2+2xy+y^2

Then you subtract y^2 from both sides: x^2+2yx+y^2-y^2=x*2+2xy+y^2-y^2

After that, you simplify: x^2+2yx=x*2+2xy

And subtract x^2+2xy from both sides: x^2+2yx-(x*2+2xy) =x*2+2xy-(x*2+2xy)

Finally, you simplify to get your final answer which is x=2, x=0

Answer 2

Rules of exponents and the distributive property apply.
  (x+y)² = (x+y)·(x+y) . . . . . meaning of exponent of 2
  = x·(x+y) +y·(x+y) . . . . . . . distributive property
  = x·x +x·y +y·x +y·y . . . . . distributive property
  = x² +x·y +x·y +y² . . . . . . meaning of exponent of 2, commutative property of multiplication
  = x² +(1+1)·x·y +y² . . . . . . distributive property
  = x²+2xy+y² . . . . . . . . . the desired form
Thus
  (x+y)² = x²+2xy+y²