Justify xz+zy=xy
however, the distributive property justifies
xz+zy = (x+y)z
To justify the equation xz + zy = xy, we need to show that both sides of the equation are equal.
Starting with the left side of the equation:
xz + zy
We can factor out z:
z(x + y)
Now, looking at the right side of the equation:
xy
Since x and y are both common factors, we can also write it as:
yx
Now, comparing the left side and the right side:
z(x + y) = yx
Using the commutative property of addition, we can rewrite (x + y) as (y + x):
z(y + x) = yx
Using the distributive property, we can expand the left side of the equation:
zy + zx = yx
Now, notice that we have the same terms on both sides of the equation. We can see that the equation holds true and is justified:
zy + zx = yx
Therefore, xz + zy = xy is justified.
To justify the equation xz+zy=xy, we need to show that it holds true for any values of x, y, and z.
To prove this, let's start by simplifying the equation:
xz + zy = xy
Now, let's take the common factor out on the left side:
z(x + y) = xy
Divide both sides by (x + y):
z = xy / (x + y)
Now, let's analyze the equation:
If (x + y) = 0, the equation would be undefined, as division by zero is not allowed in mathematics.
But if (x + y) ≠ 0, then the equation z = xy / (x + y) holds true.
Therefore, we can conclude that for any values of x, y, and z, the equation xz + zy = xy holds true, as long as (x + y) ≠ 0.