Distributive Property
a(b + c) = ab + ac; a number outside the parenthesis can be multiplied to each term within the parenthesis
The distributive property is a mathematical rule that simplifies the process of multiplying a sum by a factor. It states that multiplying a sum by a factor results in the same answer as multiplying each addend in the sum by the factor and then adding the products.
In algebraic terms, if a, b, and c are real numbers, then:
a x (b + c) = (a x b) + (a x c)
In words, this means that if you have a number (a) multiplied by the sum of two other numbers (b and c), you can simplify the expression by multiplying each addend (b and c) by the factor (a) and then adding the products together.
For example, let’s say we need to evaluate the expression 4 x (7 + 3). We can use the distributive property to simplify this expression:
4 x (7 + 3) = (4 x 7) + (4 x 3)
= 28 + 12
= 40
Therefore, 4 x (7 + 3) = 40.
The distributive property is a useful tool in algebraic simplification, particularly when working with polynomials and factoring expressions. It can also be used to simplify mental calculations and solve word problems involving multiplication.
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