describe the picture you would get by graphing the solutions(if there are any!) to the equation (x+y)^2=x^2+y^2
since (x+y)^2 = x^2+2xy+y^2, you have
2xy = 0
just the two axes.
can u explain that a little further steve?
To describe the picture that would result from graphing the solutions to the equation (x+y)^2 = x^2 + y^2, we need to first simplify the equation.
Expanding (x+y)^2, we get:
x^2 + 2xy + y^2 = x^2 + y^2
Next, we cancel out x^2 and y^2 on both sides of the equation:
2xy = 0
To solve for y, we divide both sides by 2x (assuming x is not equal to 0):
y = 0
This means that the equation (x+y)^2 = x^2 + y^2 represents a straight line on the graph, where y = 0. The line would be horizontal and intersect the x-axis. Any point on this line would satisfy the original equation.
Therefore, the picture you would get by graphing the solutions to this equation is a horizontal line passing through the x-axis.