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Algebra1

by Kenzzi
(Ohio)











































Simplify the following problem using the distributive property: 6x + 4y + 3(x – y) – 5x. Show each step in your calculation. Justify each of your steps using number properties.

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Oct 05, 2011
Simplify Algebraic Expression
by: Staff


Question:

by Kenzzi
(Ohio)


Simplify the following problem using the distributive property: 6x + 4y + 3(x - y) - 5x. Show each step in your calculation. Justify each of your steps using number properties.


Answer:


6x + 4y + 3(x - y) - 5x


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The Distributive Law allows you to simplify an algebraic expression by combining the following two operations: multiplication and addition.

It is formally defined as “the distribution of multiplication over addition”.

It is used to simplify an expression containing parentheses to an expression without parentheses.

The Distributive Law can be illustrated as follows:

a * (b + c) = a * b + a * c

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You can apply the Distributive Law to your expression as shown below:

6x + 4y + 3(x - y) - 5x

= 6x + 4y + 3 * (x - y) - 5x

= 6x + 4y + 3 * x - 3 * y - 5x

= 6x + 4y + 3x - 3y - 5x


The next step is to combine like terms in your expression.

Rearrange the terms so that like terms are grouped together (group all the terms containing y together, and all the terms containing x together).

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Associative Property of Addition:

Any series of addends can be grouped in any way and added in any order without changing the results.

This can be illustrated as follows:

2 + (6 + 8) = (2 + 6) + 8 = (2 + 8) + 6
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You can apply the Associative Law to your expression as shown below:


= 6x + 4y + 3x - 3y - 5x

= 6x + 3x - 5x + 4y - 3y

= (6x + 3x - 5x) + (4y - 3y)


Combine like terms

= (4x) + (4y - 3y)

= (4x) + (1y)

= 4x + y


The final answer is: 4x + y



Thanks for writing.

Staff
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