%5E2-expand.jpeg "(x+y+z)^2 Expand")
Expanding (x + y + z)^2
The expression (x + y + z)^2 represents the square of the sum of three variables: x, y, and z. Expanding this expression involves applying the distributive property multiple times. Here's how it works:
Understanding the Concept
The expression (x + y + z)^2 is equivalent to multiplying the sum (x + y + z) by itself:
(x + y + z)^2 = (x + y + z) * (x + y + z)
Applying the Distributive Property
To expand the expression, we need to distribute each term in the first set of parentheses over the second set:
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Distribute x: x * (x + y + z) = x^2 + xy + xz
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Distribute y: y * (x + y + z) = xy + y^2 + yz
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Distribute z: z * (x + y + z) = xz + yz + z^2
Combining the Terms
Now, we combine all the terms we obtained from the distribution:
x^2 + xy + xz + xy + y^2 + yz + xz + yz + z^2
Finally, we combine like terms:
x^2 + y^2 + z^2 + 2xy + 2xz + 2yz
Conclusion
Therefore, the expanded form of (x + y + z)^2 is x^2 + y^2 + z^2 + 2xy + 2xz + 2yz. This expansion can be useful in various mathematical problems, especially those involving algebraic manipulation and simplification.