Final answer:
The distributive property was verified by simplifying each side of the equation separately and confirming that both sides evaluate to the same result, which is 54.
Step-by-step explanation:
The question involves verifying a mathematical property called the Distributive Property of Multiplication over Addition, which dictates that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the results. Let's verify the property using the provided expression:
Left Side: 27*[6+(-4)]
First, we simplify inside the brackets: 6 + (-4) equals 2 because when we add two numbers with opposite signs, we subtract the smaller number from the larger one, keeping the sign of the larger number.
Now, multiply 27 by the result: 27 * 2 equals 54.
Right Side: [27*6] + [27*(-4)]
Separately multiplying 27 by 6 and by -4 gives us 162 and -108 respectively. When multiplications have opposite signs, the answer has a negative sign.
Add these two products together: 162 + (-108) which simplifies down to 54.
Both sides resulted in 54, confirming the verification of the distributive property.