The Distributive Property is a technique to be used when multiplying one value with multiple other values. It can be considered as a PEMDAS step if you want. It occurs during the multiplying stage of PEMDAS.
Example 1: Simplify: 3(4 + 5)
Using PEMDAS, the sum inside the parentheses should occur first, then the coefficient of the parentheses, namely the number 3, would be multiplied to the sum.
3(4 + 5)
3(9)
27 ★
The Distributive Property skips to multiplication by the 3 prior to the sum of 4 and 5. It violates PEMDAS, but it has been proven that the Distributive Property is still valid, as it results in the same answer.
3(4 + 5)
3(4) + 3(5)
12 + 15
27 ★
Example 2: 5(7 - 2) using PEMDAS
5(7 - 2)
5(5)
25 ★
Example 2 using the Distributive Property:
5(7 - 2)
5(7) - 5(2)
35 - 10
25 ★
Example 3: 2(8 + 6) using PEMDAS
2(8 + 6)
2(14)
28 ★
Example 3 using the Distributive Property:
2(8 + 6)
2(8) + 2(6)
16 + 12
28 ★
Hopefully you are convinced the Distributive Property does hold true always. It is used to multiply large numbers together in your head, where otherwise one might require paper and pencil to do the calculation. This is the power of the Distributive Property.
For now, the Distributive Property will be used to multiply 2 values by a third. Typically one of the two numbers inside the parentheses will be a variable. PEMDAS is skipped and the Distributive Property will be utilized instead. When you do this, remember like terms cannot be combined. Therefore your answer will remain a two-term expression until you know the value of the variable. Once you know the value of the variable, then you can compute a final answer. Until then, a two-term answer is norm.
Example 4: Simplify 5(x + 4)
5(x + 4)
5(x) + 5(4)
5x + 20 ★
Example 5: Simplify 3(x + 7)
3(x + 7)
3(x) + 3(7)
3x + 21 ★
Example 6: Simplify 2(x + 4)
2(x + 4)
2(x) + 2(4)
2x + 8 ★
Example 7: Simplify 4(x - 5)
4(x - 5)
4(x) - 4(5)
4x - 20 ★
Example 8: Simplify 6(x - 8)
6(x - 8)
6(x) - 6(8)
6x - 48 ★
Example 9: Simplify -3(x + 5)
-3(x + 5)
-3(x) + (-3)(5)
-3x + -15
-3x - 15 ★
Example 10: Simplify -4(x - 7)
-4(x - 7)
-4(x) - (-4)(7)
-4x - -28
-4x + 28 ★
Now try a few on your own. Type your answer into the space provided then click submit.
Example 1: Simplify: 4(x + 3)
Example 2: Simplify: 2(x + 4)
Example 3: Simplify: -5(x + 3)
Example 4: Simplify: -4(x - 7)
Example 5: Simplify: -6(x - 1)