The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.

a(b +c) = ab +ac . . . . expression of the distributive property

When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.

Below, we have written each expression using two different common factors.

27x +24x = x(27 +24) = 3x(9 +8)

0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)

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<em>Additional comment</em>

Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.

The Euclidean Algorithm can also be useful for finding common factors.

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3 years ago