What is the distributive property concerned with?

The distributive property is a fundamental principle in arithmetic that states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately and then adding the results. This means that if you have an expression like ( a(b + c) ), you can distribute ( a ) to both ( b ) and ( c ), resulting in ( ab + ac ). This property is especially useful when simplifying algebraic expressions or solving equations, as it allows for easier computation and manipulation of terms.

For instance, if ( a = 2 ), ( b = 3 ), and ( c = 4 ), using the distributive property:

[ 2(3 + 4) = 2 \times 7 = 14 ]

And applying the property directly would give:

[ 2 \times 3 + 2 \times 4 = 6 + 8 = 14 ]

Both methods yield the same result, confirming that the distributive property effectively distributes multiplication over addition.