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True or False3x + 3y = 3(x+y) is the distributive property of multiplication over addition

Question

True or False

The equation 3x + 3y = 3(x+y) is the distributive property of multiplication over addition.

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Solution

Analyzing the Statement

  1. Understanding the Expression
    The equation given is 3x+3y=3(x+y)3x + 3y = 3(x+y).

  2. Recalling the Distributive Property
    The distributive property states that a(b+c)=ab+aca(b + c) = ab + ac.

  3. Applying the Distributive Property
    In the expression 3(x+y)3(x+y), by applying the distributive property, we get: 3(x+y)=3x+3y 3(x + y) = 3x + 3y

  4. Comparing Both Sides
    The left side 3x+3y3x + 3y is equal to the right side 3(x+y)3(x+y).

Conclusion

Since both sides of the equation are equal, the statement 3x+3y=3(x+y)3x + 3y = 3(x+y) is indeed an expression of the distributive property of multiplication over addition.

Final Answer

True. The equation demonstrates the distributive property of multiplication over addition.

This problem has been solved

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