Is there a specific method or strategy to simplify complicated algebraic expressions that involve multiplication and division? Can you provide an example to help understand the process?
Yes, there are several strategies to simplify complicated algebraic expressions involving multiplication and division. One common method is to apply the rules of operations, such as the distributive property, and combine like terms.
Let's consider an example to illustrate the process:
Example: Simplify the expression 4x(3y + 2) - 2xy(5 - x)
Step 1: Distribute the multiplication.
Distribute 4x to each term inside the parentheses: 4x * 3y + 4x * 2
Distribute -2xy to each term inside the parentheses: -2xy * 5 - (-2xy * x)
The expression becomes: 12xy + 8x - 10xy + 2x^2y
Step 2: Combine like terms.
Combine the terms that have the same variables raised to the same power: 12xy - 10xy + 8x + 2x^2y
Combine the like terms: (12xy - 10xy) + (8x) + (2x^2y)
Simplify: 2xy + 8x + 2x^2y
So, the simplified form of the expression 4x(3y + 2) - 2xy(5 - x) is 2xy + 8x + 2x^2y.
By applying the distributive property and combining like terms, we have simplified the given expression.
Yes, there are specific methods and strategies to simplify complicated algebraic expressions involving multiplication and division. One common approach is to use the distributive property, which allows you to simplify expressions by distributing multiplication across addition or subtraction. You can also combine like terms by adding or subtracting.
Let me provide an example to illustrate this process:
Suppose we have the expression: 3x(y - 2) + 4x(2 - y)
To simplify this expression, we can follow these steps:
Step 1: Distribute the multiplication across the parentheses.
- Multiply 3x by each term inside the first set of parentheses: 3x * y = 3xy, and 3x * -2 = -6x.
- Similarly, multiply 4x by each term inside the second set of parentheses: 4x * 2 = 8x, and 4x * -y = -4xy.
After distributing the multiplication, we have the following expression: 3xy - 6x + 8x - 4xy.
Step 2: Combine like terms.
- We can combine the terms that have the same variable and exponent. In this case, we have 3xy and -4xy, which can be combined to give -xy.
- Similarly, we have -6x + 8x, which can be combined to give 2x.
After combining the like terms, our simplified expression becomes: -xy + 2x.
Therefore, the original complicated expression 3x(y - 2) + 4x(2 - y) simplifies to -xy + 2x.
By using the distributive property and combining like terms, we can simplify complicated algebraic expressions involving multiplication and division to obtain a more concise form of the expression.