The equation 2XZ=Y(X+Z) is a mathematical statement that involves the variables X, Y, and Z. It means that when you multiply the product of X and Z by 2, it will equal the product of Y and the sum of X and Z. This equation is known as an identity, meaning it holds true for all values of X, Y, and Z.
Proving this equation is important because it helps to solidify our understanding of algebraic concepts and principles. It also allows us to use this equation in various mathematical problems and applications.
To prove 2XZ=Y(X+Z), we need to use the distributive property of multiplication, which states that a(b+c)=ab+ac. Using this property, we can expand the right side of the equation to YX+YZ. Then, we can rearrange the terms to get 2XZ=YX+YZ. Finally, we can factor out an X from the right side to get 2XZ=X(Y+Z). Since we know that X and Y+Z are equivalent, we can replace Y+Z with X to get 2XZ=Y(X+Z).
Yes, this equation can also be proven using the associative property of multiplication, which states that a(bc)=(ab)c. By using this property, we can rearrange the terms on the left side of the equation to get (2X)Z. Then, we can expand the parentheses to get YX+YZ, which is equivalent to the right side of the equation.
This equation can be used in various real-life scenarios, such as calculating the total cost of items with a discount or finding the area of a rectangle with a missing side length. It can also be applied in engineering and physics to solve equations involving multiple variables.