Distributive Property

How to Simplify Algebraic Expressions

Distributive Property - How it Works - Video

Example 1

Example 1:

We have to distribute the term outside the parenthesis to each term in the parenthesis. So our first step is distribute or multiply the 2 or +2 to the +3x and -5 and that yields +6x -10. Now we have +6x - 10 + 5x + 2. Now we arrange the terms so the like terms are next to each other to get +6x + 5x - 10 + 2.

Now we combine +6x + 5x to get +11x and we combine -10 + 2 to get -8. So our final answer is 11x - 8.

Example 2

Example 2:

We have to distribute the term outside the parenthesis to each term in the parenthesis. So our first step is distribute or multiply the -1 to the +6 and -3xy^2 and that yields -6 + 3xy^2. Now we have +4xy^2 - 6 + 3xy^2. Now we arrange the terms so the like terms are next to each other to get +4xy^2 + 3xy^2 - 6.

Now we combine +4xy^2 + 3xy^2 to get +7xy^2 . Since -6 is the only integer, we can't combine it to anything. So our final answer is 7xy^2 - 6.

Example 3

Example 3:

We have to distribute the term outside the parenthesis to each term in the parenthesis. So our first step is distribute or multiply the 2 or +2 to the +3x and -4x^2y^2 and that yields +6x - 8x^2y^2. Now we have +10x^2y^2 + 6x - 8x^2y^2. Now we arrange the terms so the like terms are next to each other to get +10x^2y^2 - 8x^2y^2 + 6x.

Now we combine +10x^2y^2 - 8x^2y^2 to get +2x^2y^2 . Since +6x is the only term, we can't combine it to anything. So our final answer is 2x^2y^2 + 6x.

Example 4

Example 4:

We have to distribute the term outside the parenthesis to each term in the parenthesis. So our first step is distribute or multiply the 4x^2 or +4x^2 to the +3xy and -2y^2 and that yields +12x^3y - 8x^2y^2. Now we have +10x^3y + 12x^3y - 8x^2y^2. This time we don't have to rearrange the terms.

Now we combine +10x^3y + 12x^2y^2 to get +22x^3y . Since -8x^2y^2 is the only term, we can't combine it to anything. So our final answer is 22x^3y - 8x^2y^2.

Live Worksheet

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