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Identify the property that justifies the statement. (5 + 7)6= 30 + 42

Question:

Identify the property that justifies the statement.

(5 + 7)6= 30 + 42

Distributive Property

An algebraic expression is an expression which consists of constants, variables and algebraic operations like addition, subtraction, product and division.

Algebraic expressions follow distributive law.

If there are two linear algebraic expressions as

{eq}\displaystyle f(x)\ =\ ax\ +\ b\\ \displaystyle g(x)\ =\ cx\ +\ d {/eq}

then according to the distributive property, their product can be written as

{eq}\displaystyle f(x)\ \times\ g(x)\ =\ (ax\ +\ b)\ \times\ ( cx\ +\ d)\ =\ ax\ \times\ (cx\ +\ d)\ +\ b\ \times\ (cx\ +\ d) {/eq}

Commutative Property

According to the Commutative Property, if any operation is operated between two numbers, let's say a and b then the result will be same if it is applied between b and a.

Mathematically, according to this property,

{eq}\displaystyle a\ f\ b\ =\ b\ f\ a {/eq}

where:

  • f is the operation like addition or multiplication

Associative Property

We can multiply or add three or more than three numbers without considering the positions of the numbers.

For example, if we have three numbers as, a, b and c then using this property we can write

{eq}\displaystyle a\ +\ (b\ +\ c)\ =\ (a\ +\ b)\ +\ c\ =\ (a\ +\ c)\ +\ b\\ \displaystyle a\ \times\ (b\ \times\ c)\ =\ (a\ \times\ b)\ \times\ c\ =\ (a\ \times\ c)\ \times\ b {/eq}

Answer and Explanation:

Here,

  • Let a = 5, b = 7, c = 6

then we have

{eq}\displaystyle (a\ +\ b)c\ =\ ac\ +\ bc {/eq}

This shows that it is the distributive property of multiplication over addition.


Learn more about this topic:

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Distributive Property: Definition, Use & Examples

from High School Algebra II: Help and Review

Chapter 2 / Lesson 20
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