Describe how to use the distributive property and solve expressions
The distributive property is a mathematical law that states that multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products. For example, the distributive property of multiplication over addition can be written as:
a(b + c) = ab + ac
To use the distributive property and solve expressions, follow these steps:
1. Identify the terms in the expression that can be combined. For example, in the expression 3(x + 2), the terms that can be combined are x and 2.
2. Apply the distributive property to the terms that can be combined. In the expression 3(x + 2), we can distribute the 3 to both x and 2:
3(x + 2) = 3x + 6
3. Simplify the expression by combining like terms. In the expression 3x + 6, there are no like terms to combine.
4. The final result is 3x + 6.
Another example:
To solve 2(3a + 4) using the distributive property, we can distribute the 2 to both 3a and 4:
2(3a + 4) = 6a + 8
The final result is 6a + 8.
In summary, the distributive property is a helpful tool for simplifying expressions by breaking them down into smaller parts and then combining them. By following the steps outlined above, you can effectively use the distributive property to solve expressions.