Using the Distributive PropertyThe distributive property is used A LOT in Algebra! It is essential that you MASTER this skill in order to solve algebraic equations. First we are going to make sure that you have the proper background knowledge, so let's look at a simple math problem: 2( 3+4) = ?
2( 7) = 14
Since this problem contains all numerals, we can use the order of operations and solve inside the parenthesis first. We know that 3 + 4 = 7 and then multiply 7 by 2 and we get our answer of 14! That's basic math.
But, in Algebra we often don't know one of the numeric values and a variable (letter) is used in it's place. Let's look at another example: 2(x+4) = ?
In this problem, we don't know the value of x, so we can't add x + 4. But... we do want to simplify it a little further by removing the parenthesis. So, this is when the distributive property comes in! To prove that this property works, look at the model below.
Here's a couple of other examples for you to study. Copy the examples onto your paper and do them with me. More Examples
TIP: When you simplify algebraic expressions, you DO NOT want two math symbols following each other! For example: -3x + (-4) is incorrect. See how the plus sign is followed by the negative sign? This is better read as -3x - 4. -3x - (-4) is incorrect. See how the minus sign is followed by the negative sign? This is better read as -3x + 4. If you have two math symbols following each other, change the math sign to it's opposite (plus to minus or minus to plus)and change the negative sign following to a positive! Subtracting a negative is the same as adding a positive. Adding a negative is the same as subtracting a positive.
Click here to try some practice problems.
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