The expression \(2(x + y) + 2x + 2y\) can be simplified to illustrate the distributive property and combining like terms.
Here's how it works:
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Distributive Property: The term \(2(x + y)\) applies the distributive property, distributing the 2 to both \(x\) and \(y\): \[ 2(x + y) = 2x + 2y \]
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Combining Like Terms: After applying the distributive property, you can combine like terms in the expression: \[ 2x + 2y + 2x + 2y = 4x + 4y \]
Thus, this entire expression exemplifies the distributive property as well as the concept of combining like terms.